mirror of https://github.com/CGAL/cgal
Merge branch 'CGAL-Solver-package-GF-old' into CGAL-Solver-package-GF
This commit is contained in:
Simon Giraudot
commit
63f77a05a5
|
|
@ -18,8 +18,8 @@
|
|||
//
|
||||
// Author(s) : Kaspar Fischer <fischerk@inf.ethz.ch>
|
||||
|
||||
#include <CGAL/eigen_2.h>
|
||||
#include <CGAL/eigen.h>
|
||||
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <CGAL/Approximate_min_ellipsoid_d.h>
|
||||
|
||||
|
|
@ -150,34 +150,32 @@ namespace CGAL {
|
|||
{
|
||||
CGAL_APPEL_ASSERT(d==2);
|
||||
|
||||
typedef Simple_cartesian<double> K;
|
||||
typedef Vector_2<K> Vector_2;
|
||||
|
||||
// write matrix M' as [ a, b; b, c ]:
|
||||
const double matrix[3] = { E->matrix(0, 0), // a
|
||||
E->matrix(0, 1), // b
|
||||
E->matrix(1, 1) }; // c
|
||||
|
||||
std::pair<Vector_2, Vector_2> eigenvectors; // Note: not neces. normalized.
|
||||
std::pair<double, double> eigenvalues; // Note: sorted descendent.
|
||||
internal::eigen_symmetric_2<K>(matrix, eigenvectors, eigenvalues);
|
||||
const CGAL::cpp11::array<double, 3> matrix = {{ E->matrix(0, 0), // a
|
||||
E->matrix(0, 1), // b
|
||||
E->matrix(1, 1) }}; // c
|
||||
CGAL::cpp11::array<double, 4> eigenvectors; // Note: not neces. normalized.
|
||||
CGAL::cpp11::array<double, 2> eigenvalues; // Note: sorted ascendent.
|
||||
|
||||
CGAL::Default_diagonalize_traits<double, 2>::diagonalize_selfadjoint_covariance_matrix
|
||||
(matrix, eigenvalues, eigenvectors);
|
||||
|
||||
// normalize eigenvectors:
|
||||
double l1=1.0/std::sqrt(eigenvectors.first.x()*eigenvectors.first.x()+
|
||||
eigenvectors.first.y()*eigenvectors.first.y());
|
||||
double l2=1.0/std::sqrt(eigenvectors.second.x()*eigenvectors.second.x()+
|
||||
eigenvectors.second.y()*eigenvectors.second.y());
|
||||
double l1=1.0/std::sqrt(eigenvectors[2]*eigenvectors[2]+
|
||||
eigenvectors[3]*eigenvectors[3]);
|
||||
double l2=1.0/std::sqrt(eigenvectors[0]*eigenvectors[0]+
|
||||
eigenvectors[1]*eigenvectors[1]);
|
||||
|
||||
// store axes lengths:
|
||||
lengths_.push_back(std::sqrt(factor/eigenvalues.first));
|
||||
lengths_.push_back(std::sqrt(factor/eigenvalues.second));
|
||||
lengths_.push_back(std::sqrt(factor/eigenvalues[1]));
|
||||
lengths_.push_back(std::sqrt(factor/eigenvalues[0]));
|
||||
|
||||
// store directions:
|
||||
directions_.resize(2);
|
||||
directions_[0].push_back(eigenvectors.first.x()*l1);
|
||||
directions_[0].push_back(eigenvectors.first.y()*l1);
|
||||
directions_[1].push_back(eigenvectors.second.x()*l2);
|
||||
directions_[1].push_back(eigenvectors.second.y()*l2);
|
||||
directions_[0].push_back(eigenvectors[2]*l1);
|
||||
directions_[0].push_back(eigenvectors[3]*l1);
|
||||
directions_[1].push_back(eigenvectors[0]*l2);
|
||||
directions_[1].push_back(eigenvectors[1]*l2);
|
||||
}
|
||||
|
||||
template<class Traits>
|
||||
|
|
@ -192,16 +190,18 @@ namespace CGAL {
|
|||
// M' = [ b d e ]
|
||||
// [ c e f ]
|
||||
//
|
||||
const double matrix[6] = { E->matrix(0, 0), // a
|
||||
E->matrix(0, 1), // b
|
||||
E->matrix(1, 1), // d
|
||||
E->matrix(0, 2), // c
|
||||
E->matrix(1, 2), // e
|
||||
E->matrix(2, 2) }; // f
|
||||
const CGAL::cpp11::array<double, 6> matrix = {{ E->matrix(0, 0), // a
|
||||
E->matrix(0, 1), // b
|
||||
E->matrix(0, 2), // c
|
||||
E->matrix(1, 1), // d
|
||||
E->matrix(1, 2), // e
|
||||
E->matrix(2, 2) }}; // f
|
||||
|
||||
double eigenvectors[3 * 3]; // Note: not necessarily normalized.
|
||||
double eigenvalues[3]; // Note: sorted descendent.
|
||||
internal::eigen_symmetric<double>(matrix, 3, eigenvectors, eigenvalues);
|
||||
CGAL::cpp11::array<double, 9> eigenvectors; // Note: not necessarily normalized.
|
||||
CGAL::cpp11::array<double, 3> eigenvalues; // Note: sorted ascendent.
|
||||
|
||||
CGAL::Default_diagonalize_traits<double, 3>::diagonalize_selfadjoint_covariance_matrix
|
||||
(matrix, eigenvalues, eigenvectors);
|
||||
|
||||
// normalize eigenvectors:
|
||||
double l1 = 1.0/std::sqrt(eigenvectors[0] * eigenvectors[0]+ // x^2
|
||||
|
|
@ -220,15 +220,15 @@ namespace CGAL {
|
|||
|
||||
// store directions:
|
||||
directions_.resize(3);
|
||||
directions_[0].push_back(eigenvectors[0]*l1);
|
||||
directions_[0].push_back(eigenvectors[1]*l1);
|
||||
directions_[0].push_back(eigenvectors[2]*l1);
|
||||
directions_[0].push_back(eigenvectors[6]*l3);
|
||||
directions_[0].push_back(eigenvectors[7]*l3);
|
||||
directions_[0].push_back(eigenvectors[8]*l3);
|
||||
directions_[1].push_back(eigenvectors[3]*l2);
|
||||
directions_[1].push_back(eigenvectors[4]*l2);
|
||||
directions_[1].push_back(eigenvectors[5]*l2);
|
||||
directions_[2].push_back(eigenvectors[6]*l3);
|
||||
directions_[2].push_back(eigenvectors[7]*l3);
|
||||
directions_[2].push_back(eigenvectors[8]*l3);
|
||||
directions_[2].push_back(eigenvectors[0]*l1);
|
||||
directions_[2].push_back(eigenvectors[1]*l1);
|
||||
directions_[2].push_back(eigenvectors[2]*l1);
|
||||
}
|
||||
|
||||
template<class Traits>
|
||||
|
|
|
|||
|
|
@ -91,6 +91,7 @@ IMAGE_PATH = ${CMAKE_SOURCE_DIR}/Documentation/doc/Documentation/fig \
|
|||
${CMAKE_SOURCE_DIR}/STL_Extension/doc/STL_Extension/fig \
|
||||
${CMAKE_SOURCE_DIR}/Skin_surface_3/doc/Skin_surface_3/fig \
|
||||
${CMAKE_SOURCE_DIR}/Snap_rounding_2/doc/Snap_rounding_2/fig \
|
||||
${CMAKE_SOURCE_DIR}/Solver_interface/doc/Solver_interface/fig \
|
||||
${CMAKE_SOURCE_DIR}/Arrangement_on_surface_2/doc/Sweep_line_2/fig \
|
||||
${CMAKE_SOURCE_DIR}/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig \
|
||||
${CMAKE_SOURCE_DIR}/Boolean_set_operations_2/doc/Boolean_set_operations_2/fig \
|
||||
|
|
|
|||
|
|
@ -509,6 +509,15 @@ and the \ref PkgRidges_3 packages.
|
|||
|
||||
The \sc{Eigen} web site is <A HREF="http://eigen.tuxfamily.org">`http://eigen.tuxfamily.org`</A>.
|
||||
|
||||
\subsection thirdpartyLapack Lapack
|
||||
|
||||
\sc{Lapack} is a `Fortran` library for linear algebra.
|
||||
|
||||
In \cgal, \sc{Lapack} is an alternative to \sc{Eigen} for singular value decomposition for the \ref
|
||||
PkgJet_fitting_3 and the \ref PkgRidges_3 packages.
|
||||
|
||||
The \sc{Lapack} web site is <A HREF="http://www.netlib.org/lapack/">`http://www.netlib.org/lapack/`</A>.
|
||||
|
||||
\subsection thirdpartylibQGLViewer libQGLViewer
|
||||
|
||||
libQGLViewer is a 3D widget based on \sc{Qt} 4's `QGLWidget`. In case of \sc{Qt}5 used, libQGLViewer needs to be recompiled with the proper \sc{Qt}5 version.
|
||||
|
|
|
|||
|
|
@ -23,6 +23,7 @@ Geomview
|
|||
GraphicsView
|
||||
HalfedgeDS
|
||||
BGL
|
||||
Solver_interface
|
||||
Combinatorial_map
|
||||
Linear_cell_complex
|
||||
Interval_skip_list
|
||||
|
|
|
|||
|
|
@ -147,6 +147,7 @@ h1 {
|
|||
|
||||
\package_listing{STL_Extension}
|
||||
\package_listing{BGL}
|
||||
\package_listing{Solver_interface}
|
||||
\package_listing{Point_set_processing_3/Property_map}
|
||||
\package_listing{Circulator}
|
||||
\package_listing{Generator}
|
||||
|
|
|
|||
|
|
@ -0,0 +1,921 @@
|
|||
% please dont't modify the "arobase" string commands
|
||||
% they are used by the scripts to create the "How to cite CGAL" web page
|
||||
% thanks - Monique
|
||||
|
||||
@string{ author_create_page = 0 }
|
||||
@string{ category_create_page = 0 }
|
||||
@string{ reduced_year_create_page = 0 }
|
||||
@string{ complete_year_create_page = 0 }
|
||||
|
||||
@string{ index_file_title = "How to cite CGAL" }
|
||||
@string{ index_page_title = "How to cite CGAL" }
|
||||
|
||||
@string{ complete_biblio_file_title = "CGAL Publications sorted by year" }
|
||||
@string{ complete_biblio_page_title = "CGAL Publications sorted by year" }
|
||||
@string{ filename_complete_biblio = "how_to_cite_cgal" }
|
||||
|
||||
@string{ head_tag.end = "layout.html" }
|
||||
%@string{ header_of_contents = "header_of_contents" }
|
||||
|
||||
@string{ keyword_build_initials_index = 0 }
|
||||
@string{ keyword_put_initials_in_index = 0 }
|
||||
|
||||
@string{ keyword_write_bibtex_abstract = 0 }
|
||||
@string{ complete_biblio_write_bibtex_abstract = 0 }
|
||||
|
||||
@string{ disclaimer_2 = ""}
|
||||
@STRING{ default_header_of_body = "" }
|
||||
@STRING{ default_footer_of_contents = ""}
|
||||
@string{ index_write_author = 0 }
|
||||
@string{ keyword_write_author = 0 }
|
||||
@string{ complete_biblio_write_author = 0 }
|
||||
|
||||
@string{ index_write_date = 0 }
|
||||
@string{ keyword_write_date = 0 }
|
||||
@string{ complete_biblio_write_date = 0 }
|
||||
|
||||
|
||||
|
||||
@book{ cgal:eb-${CGAL_RELEASE_YEAR_ID}
|
||||
, title = "{CGAL} User and Reference Manual"
|
||||
, author = "{The CGAL Project}"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html"
|
||||
}
|
||||
|
||||
%%% Arithmetic and Algebra %%%
|
||||
|
||||
@incollection{cgal:h-af-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Algebraic Foundations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlgebraicFoundationsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hhkps-nt-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer and Susan Hert and Lutz Kettner and Sylvain Pion and Stefan Schirra"
|
||||
, title = "Number Types"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNumberTypesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-ma-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Modular Arithmetic"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgModularArithmeticSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-p-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Polynomial"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolynomialSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:bht-ak-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Eric Berberich and Michael Hemmer and Michael Kerber and Sylvain Lazard and Luis Pe{\~n}aranda and Monique Teillaud"
|
||||
, title = "Algebraic Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlgebraicKerneldSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Combinatorial Algorithms %%%
|
||||
|
||||
@incollection{cgal:h-msms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann"
|
||||
, title = "Monotone and Sorted Matrix Search"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMatrixSearchSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fgsw-lqps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Sven Sch{\"o}nherr and Frans Wessendorp"
|
||||
, title = "Linear and Quadratic Programming Solver"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgQPSolverSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometry Kernels %%%
|
||||
|
||||
@incollection{cgal:bfghhkps-lgk23-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Herv{\'e} Br{\"o}nnimann and Andreas Fabri and Geert-Jan Giezeman and Susan Hert and Michael Hoffmann and Lutz Kettner and Sylvain Pion and Stefan Schirra"
|
||||
, title = "{2D} and {3D} Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKernel23Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:s-gkd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Seel"
|
||||
, title = "{dD} Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKernelDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cpt-cgk2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pedro Machado Manh{\~a}es de Castro and Sylvain Pion and Monique Teillaud"
|
||||
, title = "{2D} Circular Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCircularKernel2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cclt-sgk3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pedro Machado Manh{\~a}es de Castro and Fr{\'e}d{\'e}ric Cazals and S{\'e}bastien Loriot and Monique Teillaud"
|
||||
, title = "{3D} Spherical Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSphericalKernel3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Convex Hull Algorithms %%%
|
||||
|
||||
@incollection{cgal:hs-chep2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Stefan Schirra"
|
||||
, title = "{2D} Convex Hulls and Extreme Points"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHull2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hs-ch3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Stefan Schirra"
|
||||
, title = "{3D} Convex Hulls"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHull3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hs-chdt3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Michael Seel"
|
||||
, title = "{dD} Convex Hulls and {Delaunay} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHullDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Polygons %%%
|
||||
|
||||
@incollection{cgal:gw-p2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Geert-Jan Giezeman and Wieger Wesselink"
|
||||
, title = "{2D} Polygons"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolygon2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fwzh-rbso2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Efi Fogel and Ron Wein and Baruch Zukerman and Dan Halperin"
|
||||
, title = "{2D} Regularized {Boolean} Set-Operations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBooleanSetOperations2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:s-bonp2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Seel"
|
||||
, title = "{2D} {Boolean} Operations on {Nef} Polygons"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNef2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hk-bonpes2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger and Lutz Kettner"
|
||||
, title = "{2D} {Boolean} Operations on {Nef} Polygons Embedded on the Sphere"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNefS2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-pp2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert"
|
||||
, title = "{2D} Polygon Partitioning"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolygonPartitioning2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:c-sspo2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Fernando Cacciola"
|
||||
, title = "{2D} Straight Skeleton and Polygon Offsetting"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgStraightSkeleton2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:w-rms2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein"
|
||||
, title = "{2D} {Minkowski} Sums"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMinkowskiSum2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Cell Complexes and Polyhedra %%%
|
||||
|
||||
@incollection{cgal:k-ps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner"
|
||||
, title = "{3D} Polyhedral Surfaces"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolyhedronSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-hds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner"
|
||||
, title = "Halfedge Data Structures"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgHDSSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-cm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Guillaume Damiand"
|
||||
, title = "Combinatorial Maps"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCombinatorialMapsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-lcc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Guillaume Damiand"
|
||||
, title = "Linear Cell Complex"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgLinearCellComplexSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hk-bonp3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger and Lutz Kettner"
|
||||
, title = "{3D} {Boolean} Operations on {Nef} Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNef3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-emspe-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger"
|
||||
, title = "Convex Decomposition of Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexDecomposition3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-msp3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger"
|
||||
, title = "{3D} {Minkowski} Sum of Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMinkowskiSum3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Arrangements %%%
|
||||
|
||||
@incollection{cgal:wfzh-a2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein and Eric Berberich and Efi Fogel and Dan Halperin and Michael Hemmer and Oren Salzman and Baruch Zukerman"
|
||||
, title = "{2D} Arrangements"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgArrangement2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:wfz-ic2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Baruch Zukerman and Ron Wein and Efi Fogel"
|
||||
, title = "{2D} Intersection of Curves"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIntersectionOfCurves2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:p-sr2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Eli Packer"
|
||||
, title = "{2D} Snap Rounding"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSnapRounding2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:w-e2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein"
|
||||
, title = "{2D} Envelopes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgEnvelope2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:mwz-e3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michal Meyerovitch and Ron Wein and Baruch Zukerman"
|
||||
, title = "{3D} Envelopes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgEnvelope3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Triangulations and Delaunay Triangulations %%%
|
||||
|
||||
@incollection{cgal:y-t2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Mariette Yvinec"
|
||||
, title = "{2D} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulation2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:py-tds2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Mariette Yvinec"
|
||||
, title = "{2D} Triangulation Data Structure"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTDS2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-pt2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Nico Kruithof"
|
||||
, title = "{2D} Periodic Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPeriodic3Triangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pt-t3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Monique Teillaud"
|
||||
, title = "{3D} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pt-tds3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Monique Teillaud"
|
||||
, title = "{3D} Triangulation Data Structure"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTDS3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ct-pt3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Manuel Caroli and Monique Teillaud"
|
||||
, title = "{3D} Periodic Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPeriodic3Triangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hdj-t-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Samuel Hornus and Olivier Devillers and Clément Jamin"
|
||||
, title = "Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulationsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-as2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Tran Kai Frank Da"
|
||||
, title = "{2D} Alpha Shapes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlphaShape2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dy-as3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Tran Kai Frank Da and Mariette Yvinec"
|
||||
, title = "{3D} Alpha Shapes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlphaShapes3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Voronoi Diagrams %%%
|
||||
|
||||
@incollection{cgal:k-sdg2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas"
|
||||
, title = "{2D} Segment {Delaunay} Graphs"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSegmentDelaunayGraph2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ky-ag2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas and Mariette Yvinec"
|
||||
, title = "{2D} {Apollonius} Graphs ({Delaunay} Graphs of Disks)"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgApolloniusGraph2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-vda2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas"
|
||||
, title = "{2D} {Voronoi} Diagram Adaptor"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgVoronoiDiagramAdaptor2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Mesh Generation %%%
|
||||
|
||||
@incollection{cgal:r-ctm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Rineau"
|
||||
, title = "{2D} Conforming Triangulations and Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMesh2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ry-smg-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Rineau and Mariette Yvinec"
|
||||
, title = "{3D} Surface Mesh Generation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMesher3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:asg-srps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Saboret and Gael Guennebaud"
|
||||
, title = "Surface Reconstruction from Point Sets"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceReconstructionFromPointSetsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-ssm3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Nico Kruithof"
|
||||
, title = "{3D} Skin Surface Meshing"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSkinSurface3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:rty-m3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Rineau and St\'ephane Tayeb and Jane Tournois and Mariette Yvinec"
|
||||
, title = "{3D} Mesh Generation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMesh_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometry Processing %%%
|
||||
|
||||
@incollection{cgal:s-ssm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Le-Jeng Andy Shiue"
|
||||
, title = "{3D} Surface Subdivision Methods"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceSubdivisionMethods3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:yl-tsms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ílker O. Yaz and S\'ebastien Loriot"
|
||||
, title = "Triangulated Surface Mesh Segmentation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceSegmentationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:c-tsms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Fernando Cacciola"
|
||||
, title = "Triangulated Surface Mesh Simplification"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMeshSimplificationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:lshxy-tsmd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sébastien Loriot, Olga Sorkine-Hornung, Yin Xu and Ilker %O. Yaz"
|
||||
, title = "Triangulated Surface Mesh Deformation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceModelingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:sal-pptsm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Saboret and Pierre Alliez and Bruno L\'evy"
|
||||
, title = "Planar Parameterization of Triangulated Surface Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceParameterizationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cp-arutsm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Marc Pouget and Fr\'ed\'eric Cazals"
|
||||
, title = "Approximation of Ridges and Umbilics on Triangulated Surface Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgRidges_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pc-eldp-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Marc Pouget and Fr\'ed\'eric Cazals"
|
||||
, title = "Estimation of Local Differential Properties of Point-Sampled Surfaces"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgJet_fitting_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ass-psp-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Saboret and Nader Salman"
|
||||
, title = "Point Set Processing"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPointSetProcessingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:m-ps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Abdelkrim Mebarki"
|
||||
, title = "{2D} Placement of Streamlines"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPlacementOfStreamlines2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Spatial Searching and Sorting %%%
|
||||
|
||||
@incollection{cgal:b-ss2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Matthias B{\"a}sken"
|
||||
, title = "{2D} Range and Neighbor Search"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPointSet2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:f-isl-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri"
|
||||
, title = "Interval Skip List"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIntervalSkipListSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:tf-ssd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Hans Tangelder and Andreas Fabri"
|
||||
, title = "{dD} Spatial Searching"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSpatialSearchingDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:n-rstd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Gabriele Neyer"
|
||||
, title = "{dD} Range and Segment Trees"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgRangeSegmentTreesDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:kmz-isiobd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner and Andreas Meyer and Afra Zomorodian"
|
||||
, title = "Intersecting Sequences of {dD} Iso-oriented Boxes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBoxIntersectionDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:atw-aabb-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and St\'ephane Tayeb and Camille Wormser"
|
||||
, title = "{3D} Fast Intersection and Distance Computation (AABB Tree)"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAABB_treeSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dd-ss-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Christophe Delage and Olivier Devillers"
|
||||
, title = "Spatial Sorting"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSpatialSortingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometric Optimization %%%
|
||||
|
||||
@incollection{cgal:fghhs-bv-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Thomas Herrmann and Michael Hoffmann and Sven Sch{\"o}nherr"
|
||||
, title = "Bounding Volumes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBoundingVolumesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hp-ia-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann and Eli Packer"
|
||||
, title = "Inscribed Areas"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgInscribedAreasSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fghhs-od-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Thomas Herrmann and Michael Hoffmann
|
||||
and Sven Sch{\"o}nherr"
|
||||
, title = "Optimal Distances"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgOptimalDistancesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ap-pcad-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Sylvain Pion and Ankit Gupta"
|
||||
, title = "Principal Component Analysis"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPrincipalComponentAnalysisDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Interpolation %%%
|
||||
|
||||
@incollection{cgal:f-i-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Julia Fl{\"o}totto"
|
||||
, title = "{2D} and Surface Function Interpolation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgInterpolation2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:abha-gbc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Dmitry Anisimov and David Bommes and Kai Hormann and Pierre Alliez"
|
||||
, title = "2D Generalized Barycentric Coordinates"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBarycentric_coordinates_2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Kinetic Data Structures %%%
|
||||
|
||||
@incollection{cgal:r-kds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Daniel Russel"
|
||||
, title = "Kinetic Data Structures"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKdsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:r-kdsf-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Daniel Russel"
|
||||
, title = "Kinetic Framework"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKdsFrameworkSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Support Library %%%
|
||||
|
||||
@incollection{cgal:hkpw-se-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann and Lutz Kettner and Sylvain Pion and Ron Wein"
|
||||
, title = "STL Extensions for {CGAL}"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgStlExtensionSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cfw-cbgl-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Fernando Cacciola and Ron Wein"
|
||||
, title = "{CGAL} and the {Boost} Graph Library"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBGLSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fs-cbpm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Laurent Saboret"
|
||||
, title = "{CGAL} and {Boost} Property Maps"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgProperty_mapSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dksy-hc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Olivier Devillers and Lutz Kettner and Michael Seel and Mariette Yvinec"
|
||||
, title = "Handles and Circulators"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgHandlesAndCirculatorsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dhhk-gog-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Olivier Devillers and Susan Hert and Michael Hoffmann and Lutz Kettner and Sven Sch{\"o}nherr"
|
||||
, title = "Geometric Object Generators"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGeneratorsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:kps-pthum-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner and Sylvain Pion and Michael Seel"
|
||||
, title = "Profiling Tools Timers, Hash Map, Union-find, Modifiers"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgProfilingToolsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fgk-ios-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Geert-Jan Giezeman and Lutz Kettner"
|
||||
, title = "IO Streams"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIOstreamsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Visualization %%%
|
||||
|
||||
@incollection{cgal:fp-gv-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Sylvain Pion"
|
||||
, title = "Geomview"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGeomviewSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fr-cqgvf-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Laurent Rineau"
|
||||
, title = "{CGAL} and the Qt Graphics View Framework "
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGraphicsViewSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:lp-gi-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "S\'ebastien Loriot and Sylvain Pion"
|
||||
, title = "{CGAL} Ipelets "
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCGALIpeletsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
|
@ -0,0 +1,931 @@
|
|||
% please dont't modify the "arobase" string commands
|
||||
% they are used by the scripts to create the "How to cite CGAL" web page
|
||||
% thanks - Monique
|
||||
|
||||
@string{ author_create_page = 0 }
|
||||
@string{ category_create_page = 0 }
|
||||
@string{ reduced_year_create_page = 0 }
|
||||
@string{ complete_year_create_page = 0 }
|
||||
|
||||
@string{ index_file_title = "How to cite CGAL" }
|
||||
@string{ index_page_title = "How to cite CGAL" }
|
||||
|
||||
@string{ complete_biblio_file_title = "CGAL Publications sorted by year" }
|
||||
@string{ complete_biblio_page_title = "CGAL Publications sorted by year" }
|
||||
@string{ filename_complete_biblio = "how_to_cite_cgal" }
|
||||
|
||||
@string{ head_tag.end = "layout.html" }
|
||||
%@string{ header_of_contents = "header_of_contents" }
|
||||
|
||||
@string{ keyword_build_initials_index = 0 }
|
||||
@string{ keyword_put_initials_in_index = 0 }
|
||||
|
||||
@string{ keyword_write_bibtex_abstract = 0 }
|
||||
@string{ complete_biblio_write_bibtex_abstract = 0 }
|
||||
|
||||
@string{ disclaimer_2 = ""}
|
||||
@STRING{ default_header_of_body = "" }
|
||||
@STRING{ default_footer_of_contents = ""}
|
||||
@string{ index_write_author = 0 }
|
||||
@string{ keyword_write_author = 0 }
|
||||
@string{ complete_biblio_write_author = 0 }
|
||||
|
||||
@string{ index_write_date = 0 }
|
||||
@string{ keyword_write_date = 0 }
|
||||
@string{ complete_biblio_write_date = 0 }
|
||||
|
||||
|
||||
|
||||
@book{ cgal:eb-${CGAL_RELEASE_YEAR_ID}
|
||||
, title = "{CGAL} User and Reference Manual"
|
||||
, author = "{The CGAL Project}"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html"
|
||||
}
|
||||
|
||||
%%% Arithmetic and Algebra %%%
|
||||
|
||||
@incollection{cgal:h-af-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Algebraic Foundations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlgebraicFoundationsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hhkps-nt-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer and Susan Hert and Lutz Kettner and Sylvain Pion and Stefan Schirra"
|
||||
, title = "Number Types"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNumberTypesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-ma-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Modular Arithmetic"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgModularArithmeticSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-p-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Polynomial"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolynomialSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:bht-ak-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Eric Berberich and Michael Hemmer and Michael Kerber and Sylvain Lazard and Luis Pe{\~n}aranda and Monique Teillaud"
|
||||
, title = "Algebraic Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlgebraicKerneldSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Combinatorial Algorithms %%%
|
||||
|
||||
@incollection{cgal:h-msms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann"
|
||||
, title = "Monotone and Sorted Matrix Search"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMatrixSearchSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fgsw-lqps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Sven Sch{\"o}nherr and Frans Wessendorp"
|
||||
, title = "Linear and Quadratic Programming Solver"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgQPSolverSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometry Kernels %%%
|
||||
|
||||
@incollection{cgal:bfghhkps-lgk23-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Herv{\'e} Br{\"o}nnimann and Andreas Fabri and Geert-Jan Giezeman and Susan Hert and Michael Hoffmann and Lutz Kettner and Sylvain Pion and Stefan Schirra"
|
||||
, title = "{2D} and {3D} Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKernel23Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:s-gkd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Seel"
|
||||
, title = "{dD} Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKernelDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cpt-cgk2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pedro Machado Manh{\~a}es de Castro and Sylvain Pion and Monique Teillaud"
|
||||
, title = "{2D} Circular Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCircularKernel2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cclt-sgk3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pedro Machado Manh{\~a}es de Castro and Fr{\'e}d{\'e}ric Cazals and S{\'e}bastien Loriot and Monique Teillaud"
|
||||
, title = "{3D} Spherical Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSphericalKernel3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Convex Hull Algorithms %%%
|
||||
|
||||
@incollection{cgal:hs-chep2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Stefan Schirra"
|
||||
, title = "{2D} Convex Hulls and Extreme Points"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHull2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hs-ch3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Stefan Schirra"
|
||||
, title = "{3D} Convex Hulls"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHull3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hs-chdt3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Michael Seel"
|
||||
, title = "{dD} Convex Hulls and {Delaunay} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHullDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Polygons %%%
|
||||
|
||||
@incollection{cgal:gw-p2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Geert-Jan Giezeman and Wieger Wesselink"
|
||||
, title = "{2D} Polygons"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolygon2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fwzh-rbso2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Efi Fogel and Ron Wein and Baruch Zukerman and Dan Halperin"
|
||||
, title = "{2D} Regularized {Boolean} Set-Operations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBooleanSetOperations2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:s-bonp2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Seel"
|
||||
, title = "{2D} {Boolean} Operations on {Nef} Polygons"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNef2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hk-bonpes2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger and Lutz Kettner"
|
||||
, title = "{2D} {Boolean} Operations on {Nef} Polygons Embedded on the Sphere"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNefS2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-pp2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert"
|
||||
, title = "{2D} Polygon Partitioning"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolygonPartitioning2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:c-sspo2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Fernando Cacciola"
|
||||
, title = "{2D} Straight Skeleton and Polygon Offsetting"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgStraightSkeleton2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:w-rms2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein"
|
||||
, title = "{2D} {Minkowski} Sums"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMinkowskiSum2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:f-ps2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri"
|
||||
, title = "{2D} Polyline Simplification"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolylineSimplification2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Cell Complexes and Polyhedra %%%
|
||||
|
||||
@incollection{cgal:k-ps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner"
|
||||
, title = "{3D} Polyhedral Surfaces"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolyhedronSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-hds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner"
|
||||
, title = "Halfedge Data Structures"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgHDSSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-cm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Guillaume Damiand"
|
||||
, title = "Combinatorial Maps"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCombinatorialMapsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-lcc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Guillaume Damiand"
|
||||
, title = "Linear Cell Complex"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgLinearCellComplexSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hk-bonp3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger and Lutz Kettner"
|
||||
, title = "{3D} {Boolean} Operations on {Nef} Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNef3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-emspe-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger"
|
||||
, title = "Convex Decomposition of Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexDecomposition3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-msp3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger"
|
||||
, title = "{3D} {Minkowski} Sum of Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMinkowskiSum3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Arrangements %%%
|
||||
|
||||
@incollection{cgal:wfzh-a2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein and Eric Berberich and Efi Fogel and Dan Halperin and Michael Hemmer and Oren Salzman and Baruch Zukerman"
|
||||
, title = "{2D} Arrangements"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgArrangement2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:wfz-ic2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Baruch Zukerman and Ron Wein and Efi Fogel"
|
||||
, title = "{2D} Intersection of Curves"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIntersectionOfCurves2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:p-sr2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Eli Packer"
|
||||
, title = "{2D} Snap Rounding"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSnapRounding2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:w-e2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein"
|
||||
, title = "{2D} Envelopes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgEnvelope2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:mwz-e3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michal Meyerovitch and Ron Wein and Baruch Zukerman"
|
||||
, title = "{3D} Envelopes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgEnvelope3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Triangulations and Delaunay Triangulations %%%
|
||||
|
||||
@incollection{cgal:y-t2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Mariette Yvinec"
|
||||
, title = "{2D} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulation2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:py-tds2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Mariette Yvinec"
|
||||
, title = "{2D} Triangulation Data Structure"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTDS2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-pt2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Nico Kruithof"
|
||||
, title = "{2D} Periodic Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPeriodic3Triangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pt-t3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Monique Teillaud"
|
||||
, title = "{3D} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pt-tds3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Monique Teillaud"
|
||||
, title = "{3D} Triangulation Data Structure"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTDS3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ct-pt3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Manuel Caroli and Monique Teillaud"
|
||||
, title = "{3D} Periodic Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPeriodic3Triangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hdj-t-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Samuel Hornus and Olivier Devillers and Clément Jamin"
|
||||
, title = "Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulationsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-as2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Tran Kai Frank Da"
|
||||
, title = "{2D} Alpha Shapes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlphaShape2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dy-as3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Tran Kai Frank Da and Mariette Yvinec"
|
||||
, title = "{3D} Alpha Shapes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlphaShapes3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Voronoi Diagrams %%%
|
||||
|
||||
@incollection{cgal:k-sdg2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas"
|
||||
, title = "{2D} Segment {Delaunay} Graphs"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSegmentDelaunayGraph2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ky-ag2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas and Mariette Yvinec"
|
||||
, title = "{2D} {Apollonius} Graphs ({Delaunay} Graphs of Disks)"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgApolloniusGraph2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-vda2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas"
|
||||
, title = "{2D} {Voronoi} Diagram Adaptor"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgVoronoiDiagramAdaptor2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Mesh Generation %%%
|
||||
|
||||
@incollection{cgal:r-ctm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Rineau"
|
||||
, title = "{2D} Conforming Triangulations and Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMesh2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ry-smg-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Rineau and Mariette Yvinec"
|
||||
, title = "{3D} Surface Mesh Generation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMesher3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:asg-srps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Saboret and Gael Guennebaud"
|
||||
, title = "Surface Reconstruction from Point Sets"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceReconstructionFromPointSetsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-ssm3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Nico Kruithof"
|
||||
, title = "{3D} Skin Surface Meshing"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSkinSurface3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:rty-m3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Rineau and St\'ephane Tayeb and Jane Tournois and Mariette Yvinec"
|
||||
, title = "{3D} Mesh Generation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMesh_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometry Processing %%%
|
||||
|
||||
@incollection{cgal:s-ssm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Le-Jeng Andy Shiue"
|
||||
, title = "{3D} Surface Subdivision Methods"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceSubdivisionMethods3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:yl-tsms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ílker O. Yaz and S\'ebastien Loriot"
|
||||
, title = "Triangulated Surface Mesh Segmentation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceSegmentationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:c-tsms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Fernando Cacciola"
|
||||
, title = "Triangulated Surface Mesh Simplification"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMeshSimplificationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:lshxy-tsmd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sébastien Loriot, Olga Sorkine-Hornung, Yin Xu and Ilker %O. Yaz"
|
||||
, title = "Triangulated Surface Mesh Deformation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceModelingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:sal-pptsm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Saboret and Pierre Alliez and Bruno L\'evy"
|
||||
, title = "Planar Parameterization of Triangulated Surface Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceParameterizationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cp-arutsm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Marc Pouget and Fr\'ed\'eric Cazals"
|
||||
, title = "Approximation of Ridges and Umbilics on Triangulated Surface Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgRidges_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pc-eldp-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Marc Pouget and Fr\'ed\'eric Cazals"
|
||||
, title = "Estimation of Local Differential Properties of Point-Sampled Surfaces"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgJet_fitting_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ass-psp-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Saboret and Nader Salman"
|
||||
, title = "Point Set Processing"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPointSetProcessingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:m-ps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Abdelkrim Mebarki"
|
||||
, title = "{2D} Placement of Streamlines"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPlacementOfStreamlines2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Spatial Searching and Sorting %%%
|
||||
|
||||
@incollection{cgal:b-ss2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Matthias B{\"a}sken"
|
||||
, title = "{2D} Range and Neighbor Search"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPointSet2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:f-isl-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri"
|
||||
, title = "Interval Skip List"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIntervalSkipListSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:tf-ssd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Hans Tangelder and Andreas Fabri"
|
||||
, title = "{dD} Spatial Searching"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSpatialSearchingDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:n-rstd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Gabriele Neyer"
|
||||
, title = "{dD} Range and Segment Trees"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgRangeSegmentTreesDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:kmz-isiobd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner and Andreas Meyer and Afra Zomorodian"
|
||||
, title = "Intersecting Sequences of {dD} Iso-oriented Boxes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBoxIntersectionDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:atw-aabb-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and St\'ephane Tayeb and Camille Wormser"
|
||||
, title = "{3D} Fast Intersection and Distance Computation (AABB Tree)"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAABB_treeSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dd-ss-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Christophe Delage and Olivier Devillers"
|
||||
, title = "Spatial Sorting"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSpatialSortingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometric Optimization %%%
|
||||
|
||||
@incollection{cgal:fghhs-bv-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Thomas Herrmann and Michael Hoffmann and Sven Sch{\"o}nherr"
|
||||
, title = "Bounding Volumes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBoundingVolumesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hp-ia-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann and Eli Packer"
|
||||
, title = "Inscribed Areas"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgInscribedAreasSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fghhs-od-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Thomas Herrmann and Michael Hoffmann
|
||||
and Sven Sch{\"o}nherr"
|
||||
, title = "Optimal Distances"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgOptimalDistancesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ap-pcad-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Sylvain Pion and Ankit Gupta"
|
||||
, title = "Principal Component Analysis"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPrincipalComponentAnalysisDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Interpolation %%%
|
||||
|
||||
@incollection{cgal:f-i-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Julia Fl{\"o}totto"
|
||||
, title = "{2D} and Surface Function Interpolation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgInterpolation2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:abha-gbc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Dmitry Anisimov and David Bommes and Kai Hormann and Pierre Alliez"
|
||||
, title = "2D Generalized Barycentric Coordinates"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBarycentric_coordinates_2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Kinetic Data Structures %%%
|
||||
|
||||
@incollection{cgal:r-kds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Daniel Russel"
|
||||
, title = "Kinetic Data Structures"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKdsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:r-kdsf-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Daniel Russel"
|
||||
, title = "Kinetic Framework"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKdsFrameworkSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Support Library %%%
|
||||
|
||||
@incollection{cgal:hkpw-se-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann and Lutz Kettner and Sylvain Pion and Ron Wein"
|
||||
, title = "STL Extensions for {CGAL}"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgStlExtensionSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cfw-cbgl-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Fernando Cacciola and Ron Wein"
|
||||
, title = "{CGAL} and the {Boost} Graph Library"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBGLSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fs-cbpm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Laurent Saboret"
|
||||
, title = "{CGAL} and {Boost} Property Maps"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgProperty_mapSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dksy-hc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Olivier Devillers and Lutz Kettner and Michael Seel and Mariette Yvinec"
|
||||
, title = "Handles and Circulators"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgHandlesAndCirculatorsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dhhk-gog-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Olivier Devillers and Susan Hert and Michael Hoffmann and Lutz Kettner and Sven Sch{\"o}nherr"
|
||||
, title = "Geometric Object Generators"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGeneratorsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:kps-pthum-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner and Sylvain Pion and Michael Seel"
|
||||
, title = "Profiling Tools Timers, Hash Map, Union-find, Modifiers"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgProfilingToolsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fgk-ios-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Geert-Jan Giezeman and Lutz Kettner"
|
||||
, title = "IO Streams"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIOstreamsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Visualization %%%
|
||||
|
||||
@incollection{cgal:fp-gv-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Sylvain Pion"
|
||||
, title = "Geomview"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGeomviewSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fr-cqgvf-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Laurent Rineau"
|
||||
, title = "{CGAL} and the Qt Graphics View Framework "
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGraphicsViewSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:lp-gi-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "S\'ebastien Loriot and Sylvain Pion"
|
||||
, title = "{CGAL} Ipelets "
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCGALIpeletsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
|
@ -0,0 +1,932 @@
|
|||
% please dont't modify the "arobase" string commands
|
||||
% they are used by the scripts to create the "How to cite CGAL" web page
|
||||
% thanks - Monique
|
||||
|
||||
@string{ author_create_page = 0 }
|
||||
@string{ category_create_page = 0 }
|
||||
@string{ reduced_year_create_page = 0 }
|
||||
@string{ complete_year_create_page = 0 }
|
||||
|
||||
@string{ index_file_title = "How to cite CGAL" }
|
||||
@string{ index_page_title = "How to cite CGAL" }
|
||||
|
||||
@string{ complete_biblio_file_title = "CGAL Publications sorted by year" }
|
||||
@string{ complete_biblio_page_title = "CGAL Publications sorted by year" }
|
||||
@string{ filename_complete_biblio = "how_to_cite_cgal" }
|
||||
|
||||
@string{ head_tag.end = "layout.html" }
|
||||
%@string{ header_of_contents = "header_of_contents" }
|
||||
|
||||
@string{ keyword_build_initials_index = 0 }
|
||||
@string{ keyword_put_initials_in_index = 0 }
|
||||
|
||||
@string{ keyword_write_bibtex_abstract = 0 }
|
||||
@string{ complete_biblio_write_bibtex_abstract = 0 }
|
||||
|
||||
@string{ disclaimer_2 = ""}
|
||||
@STRING{ default_header_of_body = "" }
|
||||
@STRING{ default_footer_of_contents = ""}
|
||||
@string{ index_write_author = 0 }
|
||||
@string{ keyword_write_author = 0 }
|
||||
@string{ complete_biblio_write_author = 0 }
|
||||
|
||||
@string{ index_write_date = 0 }
|
||||
@string{ keyword_write_date = 0 }
|
||||
@string{ complete_biblio_write_date = 0 }
|
||||
|
||||
|
||||
|
||||
@book{ cgal:eb-${CGAL_RELEASE_YEAR_ID}
|
||||
, title = "{CGAL} User and Reference Manual"
|
||||
, author = "{The CGAL Project}"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html"
|
||||
}
|
||||
|
||||
%%% Arithmetic and Algebra %%%
|
||||
|
||||
@incollection{cgal:h-af-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Algebraic Foundations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlgebraicFoundationsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hhkps-nt-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer and Susan Hert and Lutz Kettner and Sylvain Pion and Stefan Schirra"
|
||||
, title = "Number Types"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNumberTypesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-ma-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Modular Arithmetic"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgModularArithmeticSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-p-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hemmer"
|
||||
, title = "Polynomial"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolynomialSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:bht-ak-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Eric Berberich and Michael Hemmer and Michael Kerber and Sylvain Lazard and Luis Pe{\~n}aranda and Monique Teillaud"
|
||||
, title = "Algebraic Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlgebraicKerneldSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Combinatorial Algorithms %%%
|
||||
|
||||
@incollection{cgal:h-msms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann"
|
||||
, title = "Monotone and Sorted Matrix Search"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMatrixSearchSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fgsw-lqps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Sven Sch{\"o}nherr and Frans Wessendorp"
|
||||
, title = "Linear and Quadratic Programming Solver"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgQPSolverSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometry Kernels %%%
|
||||
|
||||
@incollection{cgal:bfghhkps-lgk23-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Herv{\'e} Br{\"o}nnimann and Andreas Fabri and Geert-Jan Giezeman and Susan Hert and Michael Hoffmann and Lutz Kettner and Sylvain Pion and Stefan Schirra"
|
||||
, title = "{2D} and {3D} Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKernel23Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:s-gkd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Seel"
|
||||
, title = "{dD} Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKernelDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cpt-cgk2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pedro Machado Manh{\~a}es de Castro and Sylvain Pion and Monique Teillaud"
|
||||
, title = "{2D} Circular Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCircularKernel2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cclt-sgk3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pedro Machado Manh{\~a}es de Castro and Fr{\'e}d{\'e}ric Cazals and S{\'e}bastien Loriot and Monique Teillaud"
|
||||
, title = "{3D} Spherical Geometry Kernel"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSphericalKernel3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Convex Hull Algorithms %%%
|
||||
|
||||
@incollection{cgal:hs-chep2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Stefan Schirra"
|
||||
, title = "{2D} Convex Hulls and Extreme Points"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHull2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hs-ch3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Stefan Schirra"
|
||||
, title = "{3D} Convex Hulls"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHull3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hs-chdt3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert and Michael Seel"
|
||||
, title = "{dD} Convex Hulls and {Delaunay} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexHullDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Polygons %%%
|
||||
|
||||
@incollection{cgal:gw-p2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Geert-Jan Giezeman and Wieger Wesselink"
|
||||
, title = "{2D} Polygons"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolygon2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fwzh-rbso2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Efi Fogel and Ron Wein and Baruch Zukerman and Dan Halperin"
|
||||
, title = "{2D} Regularized {Boolean} Set-Operations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBooleanSetOperations2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:s-bonp2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Seel"
|
||||
, title = "{2D} {Boolean} Operations on {Nef} Polygons"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNef2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hk-bonpes2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger and Lutz Kettner"
|
||||
, title = "{2D} {Boolean} Operations on {Nef} Polygons Embedded on the Sphere"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNefS2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-pp2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Susan Hert"
|
||||
, title = "{2D} Polygon Partitioning"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolygonPartitioning2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:c-sspo2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Fernando Cacciola"
|
||||
, title = "{2D} Straight Skeleton and Polygon Offsetting"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgStraightSkeleton2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:w-rms2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein"
|
||||
, title = "{2D} {Minkowski} Sums"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMinkowskiSum2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Cell Complexes and Polyhedra %%%
|
||||
|
||||
@incollection{cgal:k-ps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner"
|
||||
, title = "{3D} Polyhedral Surfaces"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPolyhedronSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-hds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner"
|
||||
, title = "Halfedge Data Structures"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgHDSSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
|
||||
@incollection{cgal:bsmf-hds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Mario Botsch and Daniel Sieger and Philipp Moeller and Andreas Fabri"
|
||||
, title = "Surface Mesh"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMeshSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-cm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Guillaume Damiand"
|
||||
, title = "Combinatorial Maps"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCombinatorialMapsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-lcc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Guillaume Damiand"
|
||||
, title = "Linear Cell Complex"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgLinearCellComplexSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hk-bonp3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger and Lutz Kettner"
|
||||
, title = "{3D} {Boolean} Operations on {Nef} Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgNef3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-emspe-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger"
|
||||
, title = "Convex Decomposition of Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgConvexDecomposition3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:h-msp3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Peter Hachenberger"
|
||||
, title = "{3D} {Minkowski} Sum of Polyhedra"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMinkowskiSum3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Arrangements %%%
|
||||
|
||||
@incollection{cgal:wfzh-a2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein and Eric Berberich and Efi Fogel and Dan Halperin and Michael Hemmer and Oren Salzman and Baruch Zukerman"
|
||||
, title = "{2D} Arrangements"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgArrangement2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:wfz-ic2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Baruch Zukerman and Ron Wein and Efi Fogel"
|
||||
, title = "{2D} Intersection of Curves"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIntersectionOfCurves2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:p-sr2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Eli Packer"
|
||||
, title = "{2D} Snap Rounding"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSnapRounding2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:w-e2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ron Wein"
|
||||
, title = "{2D} Envelopes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgEnvelope2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:mwz-e3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michal Meyerovitch and Ron Wein and Baruch Zukerman"
|
||||
, title = "{3D} Envelopes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgEnvelope3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Triangulations and Delaunay Triangulations %%%
|
||||
|
||||
@incollection{cgal:y-t2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Mariette Yvinec"
|
||||
, title = "{2D} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulation2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:py-tds2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Mariette Yvinec"
|
||||
, title = "{2D} Triangulation Data Structure"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTDS2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-pt2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Nico Kruithof"
|
||||
, title = "{2D} Periodic Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPeriodic3Triangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pt-t3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Monique Teillaud"
|
||||
, title = "{3D} Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pt-tds3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sylvain Pion and Monique Teillaud"
|
||||
, title = "{3D} Triangulation Data Structure"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTDS3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ct-pt3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Manuel Caroli and Monique Teillaud"
|
||||
, title = "{3D} Periodic Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPeriodic3Triangulation3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hdj-t-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Samuel Hornus and Olivier Devillers and Clément Jamin"
|
||||
, title = "Triangulations"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgTriangulationsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:d-as2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Tran Kai Frank Da"
|
||||
, title = "{2D} Alpha Shapes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlphaShape2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dy-as3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Tran Kai Frank Da and Mariette Yvinec"
|
||||
, title = "{3D} Alpha Shapes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAlphaShapes3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Voronoi Diagrams %%%
|
||||
|
||||
@incollection{cgal:k-sdg2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas"
|
||||
, title = "{2D} Segment {Delaunay} Graphs"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSegmentDelaunayGraph2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ky-ag2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas and Mariette Yvinec"
|
||||
, title = "{2D} {Apollonius} Graphs ({Delaunay} Graphs of Disks)"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgApolloniusGraph2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-vda2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Menelaos Karavelas"
|
||||
, title = "{2D} {Voronoi} Diagram Adaptor"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgVoronoiDiagramAdaptor2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Mesh Generation %%%
|
||||
|
||||
@incollection{cgal:r-ctm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Rineau"
|
||||
, title = "{2D} Conforming Triangulations and Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMesh2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ry-smg-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Rineau and Mariette Yvinec"
|
||||
, title = "{3D} Surface Mesh Generation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMesher3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:asg-srps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Saboret and Gael Guennebaud"
|
||||
, title = "Surface Reconstruction from Point Sets"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceReconstructionFromPointSetsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:k-ssm3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Nico Kruithof"
|
||||
, title = "{3D} Skin Surface Meshing"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSkinSurface3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:rty-m3-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Rineau and St\'ephane Tayeb and Jane Tournois and Mariette Yvinec"
|
||||
, title = "{3D} Mesh Generation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgMesh_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometry Processing %%%
|
||||
|
||||
@incollection{cgal:s-ssm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Le-Jeng Andy Shiue"
|
||||
, title = "{3D} Surface Subdivision Methods"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceSubdivisionMethods3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:yl-tsms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Ílker O. Yaz and S\'ebastien Loriot"
|
||||
, title = "Triangulated Surface Mesh Segmentation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceSegmentationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:c-tsms-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Fernando Cacciola"
|
||||
, title = "Triangulated Surface Mesh Simplification"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceMeshSimplificationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:lshxy-tsmd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Sébastien Loriot, Olga Sorkine-Hornung, Yin Xu and Ilker %O. Yaz"
|
||||
, title = "Triangulated Surface Mesh Deformation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceModelingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:sal-pptsm2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Laurent Saboret and Pierre Alliez and Bruno L\'evy"
|
||||
, title = "Planar Parameterization of Triangulated Surface Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSurfaceParameterizationSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cp-arutsm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Marc Pouget and Fr\'ed\'eric Cazals"
|
||||
, title = "Approximation of Ridges and Umbilics on Triangulated Surface Meshes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgRidges_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:pc-eldp-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Marc Pouget and Fr\'ed\'eric Cazals"
|
||||
, title = "Estimation of Local Differential Properties of Point-Sampled Surfaces"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgJet_fitting_3Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ass-psp-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Laurent Saboret and Nader Salman"
|
||||
, title = "Point Set Processing"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPointSetProcessingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:m-ps-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Abdelkrim Mebarki"
|
||||
, title = "{2D} Placement of Streamlines"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPlacementOfStreamlines2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Spatial Searching and Sorting %%%
|
||||
|
||||
@incollection{cgal:b-ss2-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Matthias B{\"a}sken"
|
||||
, title = "{2D} Range and Neighbor Search"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPointSet2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:f-isl-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri"
|
||||
, title = "Interval Skip List"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIntervalSkipListSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:tf-ssd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Hans Tangelder and Andreas Fabri"
|
||||
, title = "{dD} Spatial Searching"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSpatialSearchingDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:n-rstd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Gabriele Neyer"
|
||||
, title = "{dD} Range and Segment Trees"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgRangeSegmentTreesDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:kmz-isiobd-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner and Andreas Meyer and Afra Zomorodian"
|
||||
, title = "Intersecting Sequences of {dD} Iso-oriented Boxes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBoxIntersectionDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:atw-aabb-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and St\'ephane Tayeb and Camille Wormser"
|
||||
, title = "{3D} Fast Intersection and Distance Computation (AABB Tree)"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgAABB_treeSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dd-ss-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Christophe Delage and Olivier Devillers"
|
||||
, title = "Spatial Sorting"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgSpatialSortingSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Geometric Optimization %%%
|
||||
|
||||
@incollection{cgal:fghhs-bv-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Thomas Herrmann and Michael Hoffmann and Sven Sch{\"o}nherr"
|
||||
, title = "Bounding Volumes"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBoundingVolumesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:hp-ia-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann and Eli Packer"
|
||||
, title = "Inscribed Areas"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgInscribedAreasSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fghhs-od-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Kaspar Fischer and Bernd G{\"a}rtner and Thomas Herrmann and Michael Hoffmann
|
||||
and Sven Sch{\"o}nherr"
|
||||
, title = "Optimal Distances"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgOptimalDistancesSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:ap-pcad-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Pierre Alliez and Sylvain Pion and Ankit Gupta"
|
||||
, title = "Principal Component Analysis"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgPrincipalComponentAnalysisDSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Interpolation %%%
|
||||
|
||||
@incollection{cgal:f-i-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Julia Fl{\"o}totto"
|
||||
, title = "{2D} and Surface Function Interpolation"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgInterpolation2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:abha-gbc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Dmitry Anisimov and David Bommes and Kai Hormann and Pierre Alliez"
|
||||
, title = "2D Generalized Barycentric Coordinates"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBarycentric_coordinates_2Summary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Kinetic Data Structures %%%
|
||||
|
||||
@incollection{cgal:r-kds-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Daniel Russel"
|
||||
, title = "Kinetic Data Structures"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKdsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:r-kdsf-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Daniel Russel"
|
||||
, title = "Kinetic Framework"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgKdsFrameworkSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Support Library %%%
|
||||
|
||||
@incollection{cgal:hkpw-se-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Michael Hoffmann and Lutz Kettner and Sylvain Pion and Ron Wein"
|
||||
, title = "STL Extensions for {CGAL}"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgStlExtensionSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:cfw-cbgl-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Fernando Cacciola and Ron Wein"
|
||||
, title = "{CGAL} and the {Boost} Graph Library"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgBGLSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fs-cbpm-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Laurent Saboret"
|
||||
, title = "{CGAL} and {Boost} Property Maps"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgProperty_mapSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dksy-hc-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Olivier Devillers and Lutz Kettner and Michael Seel and Mariette Yvinec"
|
||||
, title = "Handles and Circulators"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgHandlesAndCirculatorsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:dhhk-gog-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Olivier Devillers and Susan Hert and Michael Hoffmann and Lutz Kettner and Sven Sch{\"o}nherr"
|
||||
, title = "Geometric Object Generators"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGeneratorsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:kps-pthum-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Lutz Kettner and Sylvain Pion and Michael Seel"
|
||||
, title = "Profiling Tools Timers, Hash Map, Union-find, Modifiers"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgProfilingToolsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fgk-ios-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Geert-Jan Giezeman and Lutz Kettner"
|
||||
, title = "IO Streams"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgIOstreamsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
%%% Visualization %%%
|
||||
|
||||
@incollection{cgal:fp-gv-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Sylvain Pion"
|
||||
, title = "Geomview"
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGeomviewSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:fr-cqgvf-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "Andreas Fabri and Laurent Rineau"
|
||||
, title = "{CGAL} and the Qt Graphics View Framework "
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgGraphicsViewSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
||||
@incollection{cgal:lp-gi-${CGAL_RELEASE_YEAR_ID}
|
||||
, author = "S\'ebastien Loriot and Sylvain Pion"
|
||||
, title = "{CGAL} Ipelets "
|
||||
, publisher = "{CGAL Editorial Board}"
|
||||
, edition = "{${CGAL_CREATED_VERSION_NUM}}"
|
||||
, booktitle = "{CGAL} User and Reference Manual"
|
||||
, url = "http://doc.cgal.org/${CGAL_CREATED_VERSION_NUM}/Manual/packages.html#PkgCGALIpeletsSummary"
|
||||
, year = ${CGAL_BUILD_YEAR4}
|
||||
}
|
||||
|
|
@ -24,7 +24,7 @@ the geometric classes and tools required by local
|
|||
computations.
|
||||
|
||||
\tparam SvdTraits features the linear
|
||||
algebra algorithm required by the fitting method.
|
||||
algebra algorithm required by the fitting method. The scalar type, `SvdTraits::FT`, must be the same as that of the `LocalKernel` concept : `LocalKernel::FT`.
|
||||
|
||||
\sa `Eigen_svd`
|
||||
\sa `Monge_form`
|
||||
|
|
|
|||
|
|
@ -13,7 +13,7 @@
|
|||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.3}
|
||||
\cgalPkgDependsOn{Solvers from \ref thirdpartyEigen.}
|
||||
\cgalPkgDependsOn{\ref PkgSolverSummary}
|
||||
\cgalPkgBib{cgal:pc-eldp}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgDemo{Operations on Polyhedra,polyhedron_3.zip}
|
||||
|
|
@ -25,12 +25,12 @@
|
|||
## Concepts ##
|
||||
- `DataKernel`
|
||||
- `LocalKernel`
|
||||
- `SvdTraits`
|
||||
|
||||
|
||||
## Classes ##
|
||||
- \link CGAL::Monge_via_jet_fitting::Monge_form `CGAL::Monge_via_jet_fitting< DataKernel, LocalKernel, SvdTraits>::Monge_form` \endlink
|
||||
- `CGAL::Monge_via_jet_fitting<DataKernel, LocalKernel, SvdTraits>`
|
||||
- `CGAL::Eigen_svd`
|
||||
|
||||
|
||||
## Global Functions ##
|
||||
The insert operator (operator<< ) is overloaded for the class \link CGAL::Monge_via_jet_fitting::Monge_form `Monge_form` \endlink.
|
||||
|
|
|
|||
|
|
@ -5,3 +5,4 @@ Algebraic_foundations
|
|||
Circulator
|
||||
Stream_support
|
||||
Number_types
|
||||
Solver_interface
|
||||
|
|
|
|||
|
|
@ -22,8 +22,8 @@
|
|||
#include <CGAL/Simple_cartesian.h>
|
||||
#include <CGAL/circulator.h>
|
||||
#include <CGAL/Linear_algebraCd.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/Cartesian_converter.h>
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
#include <math.h>
|
||||
#include <utility>
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
|
|
@ -362,27 +362,30 @@ compute_PCA(InputIterator begin, InputIterator end)
|
|||
// assemble covariance matrix as a
|
||||
// semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
FT covariance[6] = {xx,xy,yy,xz,yz,zz};
|
||||
FT eigen_values[3];
|
||||
FT eigen_vectors[9];
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ xx,xy,xz,yy,yz,zz }};
|
||||
CGAL::cpp11::array<FT, 3> eigen_values = {{ 0., 0., 0. }};
|
||||
CGAL::cpp11::array<FT, 9> eigen_vectors = {{ 0., 0., 0. }};
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
CGAL::internal::eigen_symmetric<FT>(covariance,3,eigen_vectors,eigen_values);
|
||||
CGAL::Default_diagonalize_traits<FT,3>::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
//store in m_pca_basis
|
||||
for (int i=0; i<3; i++)
|
||||
{
|
||||
m_pca_basis[i].first = eigen_values[i];
|
||||
m_pca_basis[i].first = eigen_values[2-i];
|
||||
}
|
||||
Vector_3 v1(eigen_vectors[0],eigen_vectors[1],eigen_vectors[2]);
|
||||
|
||||
Vector_3 v1(eigen_vectors[6],eigen_vectors[7],eigen_vectors[8]);
|
||||
m_pca_basis[0].second = v1;
|
||||
Vector_3 v2(eigen_vectors[3],eigen_vectors[4],eigen_vectors[5]);
|
||||
m_pca_basis[1].second = v2;
|
||||
Vector_3 v3(eigen_vectors[6],eigen_vectors[7],eigen_vectors[8]);
|
||||
Vector_3 v3(eigen_vectors[0],eigen_vectors[1],eigen_vectors[2]);
|
||||
m_pca_basis[2].second = v3;
|
||||
switch_to_direct_orientation(m_pca_basis[0].second,
|
||||
m_pca_basis[1].second,
|
||||
|
|
@ -524,15 +527,17 @@ compute_Monge_basis(const FT* A, Monge_form& monge_form)
|
|||
//in the new orthonormal basis (Y,Z) of the tangent plane :
|
||||
weingarten = inv *(1/det) * weingarten * change_XuXv2YZ;
|
||||
|
||||
//switch to eigen_symmetric algo for diagonalization of weingarten
|
||||
FT W[3] = {weingarten(0,0), weingarten(1,0), weingarten(1,1)};
|
||||
FT eval[2];
|
||||
FT evec[4];
|
||||
//eval in decreasing order
|
||||
CGAL::internal::eigen_symmetric<FT>(W,2,evec,eval);
|
||||
// diagonalization of weingarten
|
||||
CGAL::cpp11::array<FT,3> W = {{ weingarten(0,0), weingarten(1,0), weingarten(1,1) }};
|
||||
CGAL::cpp11::array<FT,2> eval = {{ 0., 0. }};
|
||||
CGAL::cpp11::array<FT,4> evec = {{ 0., 0., 0., 0. }};
|
||||
|
||||
Vector_3 d_max = evec[0]*Y + evec[1]*Z,
|
||||
d_min = evec[2]*Y + evec[3]*Z;
|
||||
//eval in increasing order
|
||||
CGAL::Default_diagonalize_traits<FT,2>::diagonalize_selfadjoint_covariance_matrix
|
||||
(W, eval, evec);
|
||||
|
||||
Vector_3 d_max = evec[2]*Y + evec[3]*Z,
|
||||
d_min = evec[0]*Y + evec[1]*Z;
|
||||
|
||||
switch_to_direct_orientation(d_max, d_min, normal);
|
||||
Aff_transformation change_basis (d_max[0], d_max[1], d_max[2],
|
||||
|
|
@ -548,8 +553,8 @@ compute_Monge_basis(const FT* A, Monge_form& monge_form)
|
|||
monge_form.maximal_principal_direction() = L2D_converter(this->change_world2fitting.inverse()(d_max));
|
||||
monge_form.minimal_principal_direction() = L2D_converter(this->change_world2fitting.inverse()(d_min));
|
||||
monge_form.normal_direction() = L2D_converter(this->change_world2fitting.inverse()(normal));
|
||||
monge_form.coefficients()[0] = L2D_NTconverter()(eval[0]);
|
||||
monge_form.coefficients()[1] = L2D_NTconverter()(eval[1]);
|
||||
monge_form.coefficients()[0] = L2D_NTconverter()(eval[1]);
|
||||
monge_form.coefficients()[1] = L2D_NTconverter()(eval[0]);
|
||||
}
|
||||
//end else
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,34 +0,0 @@
|
|||
/*!
|
||||
\ingroup PkgPointSetProcessingConcepts
|
||||
\cgalConcept
|
||||
Concept providing functions to extract eigenvectors and eigenvalue from
|
||||
covariance matrices represented by an array `a` as follows:
|
||||
<center>
|
||||
\f$ \begin{bmatrix}
|
||||
a[0] & a[1] & a[2] \\
|
||||
a[1] & a[3] & a[4] \\
|
||||
a[2] & a[4] & a[5] \\
|
||||
\end{bmatrix}\f$
|
||||
</center>
|
||||
\cgalHasModel `CGAL::Eigen_vcm_traits`
|
||||
*/
|
||||
class VCMTraits
|
||||
{
|
||||
public:
|
||||
/// fill `eigenvalues` with the eigenvalues of the covariance matrix represented by `cov`.
|
||||
/// Eigenvalues are sorted by increasing order.
|
||||
/// \return `true` if the operation was successful and `false` otherwise.
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<double,6>& cov,
|
||||
cpp11::array<double, 3>& eigenvalues);
|
||||
|
||||
/// Extract the eigenvector associated to the largest eigenvalue
|
||||
/// of the covariance matrix represented by `cov`.
|
||||
/// \return `true` if the operation was successful and `false` otherwise.
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<double,6>& cov,
|
||||
cpp11::array<double,3> &normal);
|
||||
};
|
||||
|
||||
|
|
@ -13,7 +13,7 @@
|
|||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.5}
|
||||
\cgalPkgDependsOn{\ref thirdpartyEigen "Eigen"}
|
||||
\cgalPkgDependsOn{\ref PkgSolverSummary}
|
||||
\cgalPkgBib{cgal:ass-psp}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgDemo{See Polyhedral Surface,polyhedron_3.zip}
|
||||
|
|
|
|||
|
|
@ -1,115 +0,0 @@
|
|||
// Copyright (c) 2014 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org).
|
||||
// You can redistribute it and/or modify it under the terms of the GNU
|
||||
// General Public License as published by the Free Software Foundation,
|
||||
// either version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Licensees holding a valid commercial license may use this file in
|
||||
// accordance with the commercial license agreement provided with the software.
|
||||
//
|
||||
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||||
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||||
//
|
||||
// $URL$
|
||||
// $Id$
|
||||
//
|
||||
// Author(s) : Jocelyn Meyron and Quentin Mérigot
|
||||
//
|
||||
|
||||
#ifndef CGAL_EIGEN_VCM_TRAITS_H
|
||||
#define CGAL_EIGEN_VCM_TRAITS_H
|
||||
|
||||
#include <Eigen/Dense>
|
||||
#include <Eigen/Eigenvalues>
|
||||
|
||||
#include <CGAL/array.h>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
/// A model of the concept `VCMTraits` using \ref thirdpartyEigen.
|
||||
/// \cgalModels `VCMTraits`
|
||||
class Eigen_vcm_traits{
|
||||
// Construct the covariance matrix
|
||||
static Eigen::Matrix3f
|
||||
construct_covariance_matrix (const cpp11::array<double,6>& cov) {
|
||||
Eigen::Matrix3f m;
|
||||
|
||||
m(0,0) = cov[0]; m(0,1) = cov[1]; m(0,2) = cov[2];
|
||||
m(1,1) = cov[3]; m(1,2) = cov[4];
|
||||
m(2,2) = cov[5];
|
||||
|
||||
m(1, 0) = m(0,1); m(2, 0) = m(0, 2); m(2, 1) = m(1, 2);
|
||||
|
||||
return m;
|
||||
}
|
||||
|
||||
// Diagonalize a selfadjoint matrix
|
||||
static bool
|
||||
diagonalize_selfadjoint_matrix (Eigen::Matrix3f &m,
|
||||
Eigen::Matrix3f &eigenvectors,
|
||||
Eigen::Vector3f &eigenvalues) {
|
||||
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigensolver(m);
|
||||
|
||||
if (eigensolver.info() != Eigen::Success) {
|
||||
return false;
|
||||
}
|
||||
|
||||
eigenvalues = eigensolver.eigenvalues();
|
||||
eigenvectors = eigensolver.eigenvectors();
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
public:
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<double,6>& cov,
|
||||
cpp11::array<double, 3>& eigenvalues)
|
||||
{
|
||||
Eigen::Matrix3f m = construct_covariance_matrix(cov);
|
||||
|
||||
// Diagonalizing the matrix
|
||||
Eigen::Vector3f eigenvalues_;
|
||||
Eigen::Matrix3f eigenvectors_;
|
||||
bool res = diagonalize_selfadjoint_matrix(m, eigenvectors_, eigenvalues_);
|
||||
|
||||
if (res)
|
||||
{
|
||||
eigenvalues[0]=eigenvalues_[0];
|
||||
eigenvalues[1]=eigenvalues_[1];
|
||||
eigenvalues[2]=eigenvalues_[2];
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
// Extract the eigenvector associated to the largest eigenvalue
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<double,6>& cov,
|
||||
cpp11::array<double,3> &normal)
|
||||
{
|
||||
// Construct covariance matrix
|
||||
Eigen::Matrix3f m = construct_covariance_matrix(cov);
|
||||
|
||||
// Diagonalizing the matrix
|
||||
Eigen::Vector3f eigenvalues;
|
||||
Eigen::Matrix3f eigenvectors;
|
||||
if (! diagonalize_selfadjoint_matrix(m, eigenvectors, eigenvalues)) {
|
||||
return false;
|
||||
}
|
||||
|
||||
// Eigenvalues are already sorted by increasing order
|
||||
normal[0]=eigenvectors(0,0);
|
||||
normal[1]=eigenvectors(1,0);
|
||||
normal[2]=eigenvectors(2,0);
|
||||
|
||||
return true;
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
#endif // CGAL_EIGEN_VCM_TRAITS_H
|
||||
|
|
@ -79,8 +79,8 @@ namespace CGAL {
|
|||
|
||||
template <class Point>
|
||||
inline void operator () (const Point &a,
|
||||
const Point &c,
|
||||
const Point &b)
|
||||
const Point &b,
|
||||
const Point &c)
|
||||
{
|
||||
internal::covariance_matrix_tetrahedron (a[0], a[1], a[2],
|
||||
b[0], b[1], b[2],
|
||||
|
|
@ -109,8 +109,8 @@ namespace CGAL {
|
|||
|
||||
template <class Point>
|
||||
inline void operator () (const Point &a,
|
||||
const Point &c,
|
||||
const Point &b)
|
||||
const Point &b,
|
||||
const Point &c)
|
||||
{
|
||||
const double vol = CGAL::volume(a, b, c, Point(CGAL::ORIGIN));
|
||||
//std::cerr << "vol = " << vol << "\n";
|
||||
|
|
@ -168,12 +168,10 @@ namespace CGAL {
|
|||
typename Polyhedron::Halfedge_around_facet_circulator
|
||||
h0 = it->facet_begin(), hf = h0--, hs = cpp11::next(hf);
|
||||
|
||||
while(1)
|
||||
while(hs != h0)
|
||||
{
|
||||
f (h0->vertex()->point(), hf->vertex()->point(),
|
||||
hs->vertex()->point());
|
||||
if (hs == h0)
|
||||
break;
|
||||
++hs; ++hf;
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -39,9 +39,12 @@ namespace CGAL {
|
|||
/// which however would result in selecting more points on sharper regions.
|
||||
/// More details are provided in \cgalCite{cgal:mog-vbcfe-11}.
|
||||
///
|
||||
/// \tparam VCM_traits is a model of `VCMTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
|
||||
/// then an overload using `Eigen_vcm_traits` is provided and this template parameter can be omitted.
|
||||
/// \sa `CGAL::compute_vcm()`
|
||||
/// \tparam VCM_traits is a model of `DiagonalizeTraits`. It can be
|
||||
/// omitted: if Eigen 3 (or greater) is available and
|
||||
/// `CGAL_EIGEN3_ENABLED` is defined then an overload using
|
||||
/// `Eigen_diagonalize_traits` is provided. Otherwise, the internal
|
||||
/// implementation `Internal_diagonalize_traits` is used.
|
||||
/// \sa CGAL::compute_vcm()`
|
||||
///
|
||||
template <class FT, class VCM_traits>
|
||||
bool
|
||||
|
|
@ -66,15 +69,15 @@ vcm_is_on_feature_edge (cpp11::array<FT,6> &cov,
|
|||
|
||||
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
template <class FT>
|
||||
bool
|
||||
vcm_is_on_feature_edge (cpp11::array<FT,6> &cov,
|
||||
double threshold)
|
||||
{
|
||||
return vcm_is_on_feature_edge(cov, threshold, Eigen_vcm_traits());
|
||||
return vcm_is_on_feature_edge(cov, threshold,
|
||||
CGAL::Default_diagonalize_traits<double, 3>());
|
||||
|
||||
}
|
||||
#endif
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
|
|
|
|||
|
|
@ -32,9 +32,7 @@
|
|||
#include <CGAL/Orthogonal_k_neighbor_search.h>
|
||||
#include <CGAL/Fuzzy_sphere.h>
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
#include <CGAL/Eigen_vcm_traits.h>
|
||||
#endif
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <iterator>
|
||||
#include <vector>
|
||||
|
|
@ -368,9 +366,11 @@ vcm_estimate_normals (ForwardIterator first, ///< iterator over the first input
|
|||
/// @tparam ForwardIterator iterator over input points.
|
||||
/// @tparam PointPMap is a model of `ReadablePropertyMap` with a value_type = `Kernel::Point_3`.
|
||||
/// @tparam NormalPMap is a model of `WritablePropertyMap` with a value_type = `Kernel::Vector_3`.
|
||||
/// \tparam VCM_traits is a model of `VCMTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
|
||||
/// then an overload using `Eigen_vcm_traits` is provided and this template parameter can be omitted.
|
||||
|
||||
/// \tparam VCM_traits is a model of `DiagonalizeTraits`. It can be
|
||||
/// omitted: if Eigen 3 (or greater) is available and
|
||||
/// `CGAL_EIGEN3_ENABLED` is defined then an overload using
|
||||
/// `Eigen_diagonalize_traits` is provided. Otherwise, the internal
|
||||
/// implementation `Internal_diagonalize_traits` is used.
|
||||
// This variant deduces the kernel from the point property map
|
||||
// and uses a radius for the convolution.
|
||||
template < typename ForwardIterator,
|
||||
|
|
@ -409,8 +409,11 @@ vcm_estimate_normals (ForwardIterator first, ///< iterator over the first input
|
|||
/// @tparam ForwardIterator iterator over input points.
|
||||
/// @tparam PointPMap is a model of `ReadablePropertyMap` with a value_type = `Kernel::Point_3`.
|
||||
/// @tparam NormalPMap is a model of `WritablePropertyMap` with a value_type = `Kernel::Vector_3`.
|
||||
/// \tparam VCM_traits is a model of `VCMTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
|
||||
/// then an overload using `Eigen_vcm_traits` is provided and this template parameter can be omitted.
|
||||
/// \tparam VCM_traits is a model of `DiagonalizeTraits`. It can be
|
||||
/// omitted: if Eigen 3 (or greater) is available and
|
||||
/// `CGAL_EIGEN3_ENABLED` is defined then an overload using
|
||||
/// `Eigen_diagonalize_traits` is provided. Otherwise, the internal
|
||||
/// implementation `Internal_diagonalize_traits` is used.
|
||||
|
||||
// This variant deduces the kernel from the point property map
|
||||
// and uses a number of neighbors for the convolution.
|
||||
|
|
@ -440,7 +443,6 @@ vcm_estimate_normals (ForwardIterator first, ///< iterator over the first input
|
|||
}
|
||||
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
template < typename ForwardIterator,
|
||||
typename PointPMap,
|
||||
typename NormalPMap
|
||||
|
|
@ -453,7 +455,8 @@ vcm_estimate_normals (ForwardIterator first,
|
|||
double offset_radius,
|
||||
double convolution_radius)
|
||||
{
|
||||
vcm_estimate_normals(first, beyond, point_pmap, normal_pmap, offset_radius, convolution_radius, Eigen_vcm_traits());
|
||||
vcm_estimate_normals(first, beyond, point_pmap, normal_pmap, offset_radius, convolution_radius,
|
||||
CGAL::Default_diagonalize_traits<double, 3>());
|
||||
}
|
||||
|
||||
template < typename ForwardIterator,
|
||||
|
|
@ -468,9 +471,11 @@ vcm_estimate_normals (ForwardIterator first,
|
|||
double offset_radius,
|
||||
unsigned int nb_neighbors_convolve)
|
||||
{
|
||||
vcm_estimate_normals(first, beyond, point_pmap, normal_pmap, offset_radius, nb_neighbors_convolve, Eigen_vcm_traits());
|
||||
vcm_estimate_normals(first, beyond, point_pmap, normal_pmap, offset_radius, nb_neighbors_convolve,
|
||||
CGAL::Default_diagonalize_traits<double, 3>());
|
||||
|
||||
}
|
||||
#endif
|
||||
|
||||
|
||||
/// @cond SKIP_IN_MANUAL
|
||||
// This variant creates a default point property map = Identity_property_map
|
||||
|
|
|
|||
|
|
@ -30,11 +30,11 @@ int main (void) {
|
|||
|
||||
std::cout << "Normal is " << points[0].second << std::endl;
|
||||
|
||||
// The normal at the origin should be (0, 0, -1)
|
||||
// The normal at the origin should be (0, 0, 1)
|
||||
double epsilon=2e-5;
|
||||
assert(points[0].second.x() < epsilon && points[0].second.x() > -epsilon);
|
||||
assert(points[0].second.y() < epsilon && points[0].second.y() > -epsilon);
|
||||
assert(points[0].second.z() < -1+epsilon && points[0].second.z() > -1-epsilon);
|
||||
assert(points[0].second.z() < 1+epsilon && points[0].second.z() > 1-epsilon);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -13,6 +13,8 @@ The tag `tag` identifies the dimension to be considered from the objects. For po
|
|||
|
||||
The class `K` is the kernel in which the value type of the `InputIterator` is defined. It can be omitted and deduced automatically from the value type.
|
||||
|
||||
The class `Diagonalize_traits` is a model of `DiagonalizeTraits`. It can be omitted: if Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined then an overload using `Eigen_diagonalize_traits` is provided. Otherwise, the internal implementation `Internal_diagonalize_traits` is used.
|
||||
|
||||
\cgalHeading{Requirements}
|
||||
|
||||
<OL>
|
||||
|
|
@ -28,14 +30,15 @@ omitted.
|
|||
|
||||
\pre first != beyond.
|
||||
*/
|
||||
template < typename InputIterator, typename K, typename Tag >
|
||||
template < typename InputIterator, typename K, typename Tag, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::Line_2 & line,
|
||||
typename K::Point_2 & centroid,
|
||||
const Tag & tag,
|
||||
const K & k);
|
||||
const K & k,
|
||||
const Diagonalize_traits& diagonalize_traits);
|
||||
|
||||
} /* namespace CGAL */
|
||||
|
||||
|
|
|
|||
|
|
@ -64,6 +64,13 @@ The class `K` is the kernel in which the
|
|||
value type of `InputIterator` is defined. It can be omitted and deduced
|
||||
automatically from the value type.
|
||||
|
||||
The class `Diagonalize_traits` is a model of `DiagonalizeTraits`. It
|
||||
can be omitted: if Eigen 3 (or greater) is available and
|
||||
`CGAL_EIGEN3_ENABLED` is defined then an overload using
|
||||
`Eigen_diagonalize_traits` is provided. Otherwise, the internal
|
||||
implementation `Internal_diagonalize_traits` is used.
|
||||
|
||||
|
||||
\cgalHeading{Requirements}
|
||||
|
||||
<OL>
|
||||
|
|
@ -77,14 +84,15 @@ automatically from the value type.
|
|||
|
||||
|
||||
*/
|
||||
template < typename InputIterator, typename K, typename Tag >
|
||||
template < typename InputIterator, typename K, typename Tag, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::Line_3& line,
|
||||
typename K::Point_3& centroid,
|
||||
const Tag& tag,
|
||||
const K& k);
|
||||
const K& k,
|
||||
const Diagonalize_traits& diagonalize_traits);
|
||||
|
||||
/*!
|
||||
\brief computes the best fitting 3D plane of a 3D object set in the
|
||||
|
|
@ -100,6 +108,12 @@ of `InputIterator` is defined. It can be omitted and deduced
|
|||
automatically from the value type. The tag `tag` identifies the
|
||||
dimension to be considered from the objects (see above).
|
||||
|
||||
The class `Diagonalize_traits` is a model of `DiagonalizeTraits`. It
|
||||
can be omitted: if Eigen 3 (or greater) is available and
|
||||
`CGAL_EIGEN3_ENABLED` is defined then an overload using
|
||||
`Eigen_diagonalize_traits` is provided. Otherwise, the internal
|
||||
implementation `Internal_diagonalize_traits` is used.
|
||||
|
||||
\cgalHeading{Requirements}
|
||||
|
||||
<OL>
|
||||
|
|
@ -112,14 +126,15 @@ dimension to be considered from the objects (see above).
|
|||
</OL>
|
||||
|
||||
*/
|
||||
template < typename InputIterator, typename K, typename Tag >
|
||||
template < typename InputIterator, typename K, typename Tag, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::Plane_3& plane,
|
||||
typename K::Point_3& centroid,
|
||||
const Tag& tag,
|
||||
const K& k);
|
||||
const K& k,
|
||||
const Diagonalize_traits& diagonalize_traits);
|
||||
|
||||
/// @}
|
||||
|
||||
|
|
|
|||
|
|
@ -27,6 +27,7 @@
|
|||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.2}
|
||||
\cgalPkgDependsOn{\ref PkgSolverSummary}
|
||||
\cgalPkgBib{cgal:ap-pcad}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgDemo{Principal Component Analysis,pca.zip,Operations on Polygons,polygon.zip,Operations on Polyhedra,polyhedron_3.zip}
|
||||
|
|
|
|||
|
|
@ -4,3 +4,4 @@ STL_Extension
|
|||
Algebraic_foundations
|
||||
Circulator
|
||||
Stream_support
|
||||
Solver_interface
|
||||
|
|
|
|||
|
|
@ -20,7 +20,6 @@
|
|||
#ifndef CGAL_LINEAR_LEAST_SQUARES_FITTING_UTIL_H
|
||||
#define CGAL_LINEAR_LEAST_SQUARES_FITTING_UTIL_H
|
||||
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/Linear_algebraCd.h>
|
||||
#include <CGAL/Dimension.h>
|
||||
|
||||
|
|
@ -52,7 +51,7 @@ template < typename InputIterator,
|
|||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K& , // kernel
|
||||
const typename K::Point_3*, // used for indirection
|
||||
|
|
@ -63,9 +62,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
typedef typename K::Vector_3 Vector;
|
||||
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
covariance[0] = covariance[1] = covariance[2] =
|
||||
covariance[3] = covariance[4] = covariance[5] = (FT)0.0;
|
||||
for(InputIterator it = first;
|
||||
|
|
@ -76,8 +75,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
Vector d = p - c;
|
||||
covariance[0] += d.x() * d.x();
|
||||
covariance[1] += d.x() * d.y();
|
||||
covariance[2] += d.y() * d.y();
|
||||
covariance[3] += d.x() * d.z();
|
||||
covariance[2] += d.x() * d.z();
|
||||
covariance[3] += d.y() * d.y();
|
||||
covariance[4] += d.y() * d.z();
|
||||
covariance[5] += d.z() * d.z();
|
||||
}
|
||||
|
|
@ -88,8 +87,8 @@ template < typename InputIterator,
|
|||
typename K >
|
||||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
InputIterator beyond,
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K&, // kernel
|
||||
const typename K::Triangle_3*,// used for indirection
|
||||
|
|
@ -102,9 +101,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
//Final combined covariance matrix for all triangles and their combined mass
|
||||
FT mass = 0.0;
|
||||
|
||||
|
|
@ -141,8 +140,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0];
|
||||
covariance[1] += transformation[1][0];
|
||||
covariance[2] += transformation[1][1];
|
||||
covariance[3] += transformation[2][0];
|
||||
covariance[2] += transformation[2][0];
|
||||
covariance[3] += transformation[1][1];
|
||||
covariance[4] += transformation[2][1];
|
||||
covariance[5] += transformation[2][2];
|
||||
|
||||
|
|
@ -153,8 +152,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (-1.0 * c.x() * c.x());
|
||||
covariance[1] += mass * (-1.0 * c.x() * c.y());
|
||||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[3] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[2] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[3] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[4] += mass * (-1.0 * c.z() * c.y());
|
||||
covariance[5] += mass * (-1.0 * c.z() * c.z());
|
||||
|
||||
|
|
@ -165,8 +164,8 @@ template < typename InputIterator,
|
|||
typename K >
|
||||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
InputIterator beyond,
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K& , // kernel
|
||||
const typename K::Iso_cuboid_3*,// used for indirection
|
||||
|
|
@ -179,9 +178,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
// final combined covariance matrix for all cuboids and their combined mass
|
||||
FT mass = (FT)0.0;
|
||||
|
||||
|
|
@ -227,8 +226,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0] + volume * (2*x0*xav0 + x0*x0);
|
||||
covariance[1] += transformation[1][0] + volume * (xav0*y0 + yav0*x0 + x0*y0);
|
||||
covariance[2] += transformation[1][1] + volume * (2*y0*yav0 + y0*y0);
|
||||
covariance[3] += transformation[2][0] + volume * (x0*zav0 + xav0*z0 + x0*z0);
|
||||
covariance[2] += transformation[2][0] + volume * (x0*zav0 + xav0*z0 + x0*z0);
|
||||
covariance[3] += transformation[1][1] + volume * (2*y0*yav0 + y0*y0);
|
||||
covariance[4] += transformation[2][1] + volume * (yav0*z0 + y0*zav0 + z0*y0);
|
||||
covariance[5] += transformation[2][2] + volume * (2*zav0*z0 + z0*z0);
|
||||
|
||||
|
|
@ -239,8 +238,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (- c.x() * c.x());
|
||||
covariance[1] += mass * (- c.x() * c.y());
|
||||
covariance[2] += mass * (- c.y() * c.y());
|
||||
covariance[3] += mass * (- c.z() * c.x());
|
||||
covariance[2] += mass * (- c.z() * c.x());
|
||||
covariance[3] += mass * (- c.y() * c.y());
|
||||
covariance[4] += mass * (- c.z() * c.y());
|
||||
covariance[5] += mass * (- c.z() * c.z());
|
||||
}
|
||||
|
|
@ -251,7 +250,7 @@ template < typename InputIterator,
|
|||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K& , // kernel
|
||||
const typename K::Iso_cuboid_3*,// used for indirection
|
||||
|
|
@ -264,9 +263,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
//Final combined covariance matrix for all cuboids and their combined mass
|
||||
FT mass = (FT)0.0;
|
||||
|
||||
|
|
@ -319,8 +318,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0] + area * (2*x0*xav0 + x0*x0);
|
||||
covariance[1] += transformation[1][0] + area * (xav0*y0 + yav0*x0 + x0*y0);
|
||||
covariance[2] += transformation[1][1] + area * (2*y0*yav0 + y0*y0);
|
||||
covariance[3] += transformation[2][0] + area * (x0*zav0 + xav0*z0 + x0*z0);
|
||||
covariance[2] += transformation[2][0] + area * (x0*zav0 + xav0*z0 + x0*z0);
|
||||
covariance[3] += transformation[1][1] + area * (2*y0*yav0 + y0*y0);
|
||||
covariance[4] += transformation[2][1] + area * (yav0*z0 + y0*zav0 + z0*y0);
|
||||
covariance[5] += transformation[2][2] + area * (2*zav0*z0 + z0*z0);
|
||||
|
||||
|
|
@ -331,8 +330,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (-1.0 * c.x() * c.x());
|
||||
covariance[1] += mass * (-1.0 * c.x() * c.y());
|
||||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[3] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[2] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[3] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[4] += mass * (-1.0 * c.z() * c.y());
|
||||
covariance[5] += mass * (-1.0 * c.z() * c.z());
|
||||
|
||||
|
|
@ -344,7 +343,7 @@ template < typename InputIterator,
|
|||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K&, // kernel
|
||||
const typename K::Sphere_3*, // used for indirection
|
||||
|
|
@ -357,9 +356,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
//Final combined covariance matrix for all spheres and their combined mass
|
||||
FT mass = 0.0;
|
||||
|
||||
|
|
@ -402,8 +401,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0] + volume * x0*x0;
|
||||
covariance[1] += transformation[1][0] + volume * x0*y0;
|
||||
covariance[2] += transformation[1][1] + volume * y0*y0;
|
||||
covariance[3] += transformation[2][0] + volume * x0*z0;
|
||||
covariance[2] += transformation[2][0] + volume * x0*z0;
|
||||
covariance[3] += transformation[1][1] + volume * y0*y0;
|
||||
covariance[4] += transformation[2][1] + volume * z0*y0;
|
||||
covariance[5] += transformation[2][2] + volume * z0*z0;
|
||||
|
||||
|
|
@ -414,8 +413,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (-1.0 * c.x() * c.x());
|
||||
covariance[1] += mass * (-1.0 * c.x() * c.y());
|
||||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[3] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[2] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[3] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[4] += mass * (-1.0 * c.z() * c.y());
|
||||
covariance[5] += mass * (-1.0 * c.z() * c.z());
|
||||
|
||||
|
|
@ -426,7 +425,7 @@ template < typename InputIterator,
|
|||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K&, // kernel
|
||||
const typename K::Sphere_3*, // used for indirection
|
||||
|
|
@ -439,9 +438,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
//Final combined covariance matrix for all spheres and their combined mass
|
||||
FT mass = 0.0;
|
||||
|
||||
|
|
@ -485,8 +484,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0] + area * x0*x0;
|
||||
covariance[1] += transformation[1][0] + area * x0*y0;
|
||||
covariance[2] += transformation[1][1] + area * y0*y0;
|
||||
covariance[3] += transformation[2][0] + area * x0*z0;
|
||||
covariance[2] += transformation[2][0] + area * x0*z0;
|
||||
covariance[3] += transformation[1][1] + area * y0*y0;
|
||||
covariance[4] += transformation[2][1] + area * z0*y0;
|
||||
covariance[5] += transformation[2][2] + area * z0*z0;
|
||||
|
||||
|
|
@ -497,8 +496,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (-1.0 * c.x() * c.x());
|
||||
covariance[1] += mass * (-1.0 * c.x() * c.y());
|
||||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[3] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[2] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[3] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[4] += mass * (-1.0 * c.z() * c.y());
|
||||
covariance[5] += mass * (-1.0 * c.z() * c.z());
|
||||
|
||||
|
|
@ -510,7 +509,7 @@ template < typename InputIterator,
|
|||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K& , // kernel
|
||||
const typename K::Tetrahedron_3*,// used for indirection
|
||||
|
|
@ -523,9 +522,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
//Final combined covariance matrix for all tetrahedrons and their combined mass
|
||||
FT mass = 0.0;
|
||||
|
||||
|
|
@ -571,8 +570,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0] + volume * (2*x0*xav0 + x0*x0);
|
||||
covariance[1] += transformation[1][0] + volume * (xav0*y0 + yav0*x0 + x0*y0);
|
||||
covariance[2] += transformation[1][1] + volume * (2*y0*yav0 + y0*y0);
|
||||
covariance[3] += transformation[2][0] + volume * (x0*zav0 + xav0*z0 + x0*z0);
|
||||
covariance[2] += transformation[2][0] + volume * (x0*zav0 + xav0*z0 + x0*z0);
|
||||
covariance[3] += transformation[1][1] + volume * (2*y0*yav0 + y0*y0);
|
||||
covariance[4] += transformation[2][1] + volume * (yav0*z0 + y0*zav0 + z0*y0);
|
||||
covariance[5] += transformation[2][2] + volume * (2*zav0*z0 + z0*z0);
|
||||
|
||||
|
|
@ -583,8 +582,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (-1.0 * c.x() * c.x());
|
||||
covariance[1] += mass * (-1.0 * c.x() * c.y());
|
||||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[3] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[2] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[3] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[4] += mass * (-1.0 * c.z() * c.y());
|
||||
covariance[5] += mass * (-1.0 * c.z() * c.z());
|
||||
}
|
||||
|
|
@ -595,7 +594,7 @@ template < typename InputIterator,
|
|||
void
|
||||
assemble_covariance_matrix_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
typename K::FT covariance[6], // covariance matrix
|
||||
CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
const K& , // kernel
|
||||
const typename K::Segment_3*,// used for indirection
|
||||
|
|
@ -608,9 +607,9 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 3 4 5
|
||||
// 0 1 2
|
||||
// 3 4
|
||||
// 5
|
||||
//Final combined covariance matrix for all segments and their combined mass
|
||||
FT mass = 0.0;
|
||||
|
||||
|
|
@ -648,8 +647,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// and add to covariance matrix
|
||||
covariance[0] += transformation[0][0];
|
||||
covariance[1] += transformation[1][0];
|
||||
covariance[2] += transformation[1][1];
|
||||
covariance[3] += transformation[2][0];
|
||||
covariance[2] += transformation[2][0];
|
||||
covariance[3] += transformation[1][1];
|
||||
covariance[4] += transformation[2][1];
|
||||
covariance[5] += transformation[2][2];
|
||||
|
||||
|
|
@ -660,8 +659,8 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// the center of mass to get the covariance.
|
||||
covariance[0] += mass * (-1.0 * c.x() * c.x());
|
||||
covariance[1] += mass * (-1.0 * c.x() * c.y());
|
||||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[3] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[2] += mass * (-1.0 * c.z() * c.x());
|
||||
covariance[3] += mass * (-1.0 * c.y() * c.y());
|
||||
covariance[4] += mass * (-1.0 * c.z() * c.y());
|
||||
covariance[5] += mass * (-1.0 * c.z() * c.z());
|
||||
|
||||
|
|
@ -671,23 +670,27 @@ assemble_covariance_matrix_3(InputIterator first,
|
|||
// compute the eigen values and vectors of the covariance
|
||||
// matrix and deduces the best linear fitting plane.
|
||||
// returns fitting quality
|
||||
template < typename K >
|
||||
template < typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
fitting_plane_3(const typename K::FT covariance[6], // covariance matrix
|
||||
fitting_plane_3(CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
typename K::Plane_3& plane, // best fit plane
|
||||
const K& ) // kernel
|
||||
const K&, // kernel
|
||||
const Diagonalize_traits& ) // Diagonalize traits
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Plane_3 Plane;
|
||||
typedef typename K::Vector_3 Vector;
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
FT eigen_values[3];
|
||||
FT eigen_vectors[9];
|
||||
eigen_symmetric<FT>(covariance,3,eigen_vectors,eigen_values);
|
||||
CGAL::cpp11::array<FT, 3> eigen_values = {{ 0. , 0., 0. }};
|
||||
CGAL::cpp11::array<FT, 9> eigen_vectors = {{ 0., 0., 0.,
|
||||
0., 0., 0.,
|
||||
0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// degenerate case
|
||||
if(eigen_values[0] == eigen_values[1] &&
|
||||
|
|
@ -700,11 +703,11 @@ fitting_plane_3(const typename K::FT covariance[6], // covariance matrix
|
|||
}
|
||||
else // regular and line case
|
||||
{
|
||||
Vector normal(eigen_vectors[6],
|
||||
eigen_vectors[7],
|
||||
eigen_vectors[8]);
|
||||
Vector normal(eigen_vectors[0],
|
||||
eigen_vectors[1],
|
||||
eigen_vectors[2]);
|
||||
plane = Plane(c,normal);
|
||||
return FT(1) - eigen_values[2] / eigen_values[1];
|
||||
return FT(1) - eigen_values[0] / eigen_values[1];
|
||||
} // end regular case
|
||||
}
|
||||
|
||||
|
|
@ -712,23 +715,27 @@ fitting_plane_3(const typename K::FT covariance[6], // covariance matrix
|
|||
// matrix and deduces the best linear fitting line
|
||||
// (this is an internal function)
|
||||
// returns fitting quality
|
||||
template < typename K >
|
||||
template < typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
fitting_line_3(const typename K::FT covariance[6], // covariance matrix
|
||||
fitting_line_3(CGAL::cpp11::array<typename K::FT, 6>& covariance, // covariance matrix
|
||||
const typename K::Point_3& c, // centroid
|
||||
typename K::Line_3& line, // best fit line
|
||||
const K&) // kernel
|
||||
const K&, // kernel
|
||||
const Diagonalize_traits& ) // Diagonalize traits
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Line_3 Line;
|
||||
typedef typename K::Vector_3 Vector;
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
FT eigen_values[3];
|
||||
FT eigen_vectors[9];
|
||||
eigen_symmetric<FT>(covariance,3,eigen_vectors,eigen_values);
|
||||
CGAL::cpp11::array<FT, 3> eigen_values = {{ 0. , 0., 0. }};
|
||||
CGAL::cpp11::array<FT, 9> eigen_vectors = {{ 0., 0., 0.,
|
||||
0., 0., 0.,
|
||||
0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// isotropic case (infinite number of directions)
|
||||
if(eigen_values[0] == eigen_values[1] &&
|
||||
|
|
@ -742,9 +749,9 @@ fitting_line_3(const typename K::FT covariance[6], // covariance matrix
|
|||
else
|
||||
{
|
||||
// regular case
|
||||
Vector direction(eigen_vectors[0],eigen_vectors[1],eigen_vectors[2]);
|
||||
Vector direction(eigen_vectors[6],eigen_vectors[7],eigen_vectors[8]);
|
||||
line = Line(c,direction);
|
||||
return (FT)1.0 - eigen_values[1] / eigen_values[0];
|
||||
return (FT)1.0 - eigen_values[1] / eigen_values[2];
|
||||
}
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -1,229 +0,0 @@
|
|||
// Copyright (c) 2005 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public License as
|
||||
// published by the Free Software Foundation; either version 3 of the License,
|
||||
// or (at your option) any later version.
|
||||
//
|
||||
// Licensees holding a valid commercial license may use this file in
|
||||
// accordance with the commercial license agreement provided with the software.
|
||||
//
|
||||
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||||
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||||
//
|
||||
// $URL$
|
||||
// $Id$
|
||||
//
|
||||
//
|
||||
// Author(s) : Bruno Levy, Pierre Alliez
|
||||
|
||||
#ifndef CGAL_EIGEN_H
|
||||
#define CGAL_EIGEN_H
|
||||
|
||||
#include <cmath>
|
||||
#include <CGAL/number_utils.h>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
namespace internal {
|
||||
|
||||
template <class FT>
|
||||
void eigen_symmetric(const FT *mat,
|
||||
const int n,
|
||||
FT *eigen_vectors,
|
||||
FT *eigen_values,
|
||||
const int MAX_ITER = 100)
|
||||
{
|
||||
static const FT EPSILON = (FT)0.00001;
|
||||
|
||||
// number of entries in mat
|
||||
int nn = (n*(n+1))/2;
|
||||
|
||||
// copy matrix
|
||||
FT *a = new FT[nn];
|
||||
int ij;
|
||||
for(ij=0; ij<nn; ij++)
|
||||
a[ij] = mat[ij];
|
||||
// Fortran-porting
|
||||
a--;
|
||||
|
||||
// init diagonalization matrix as the unit matrix
|
||||
FT *v = new FT[n*n];
|
||||
ij = 0;
|
||||
int i;
|
||||
for(i=0; i<n; i++)
|
||||
for(int j=0; j<n; j++)
|
||||
if(i==j)
|
||||
v[ij++] = 1.0;
|
||||
else
|
||||
v[ij++] = 0.0;
|
||||
// Fortran-porting
|
||||
v--;
|
||||
|
||||
// compute weight of the non diagonal terms
|
||||
ij = 1;
|
||||
FT a_norm = 0.0;
|
||||
for(i=1; i<=n; i++)
|
||||
for(int j=1; j<=i; j++)
|
||||
{
|
||||
if( i!=j )
|
||||
{
|
||||
FT a_ij = a[ij];
|
||||
a_norm += a_ij * a_ij;
|
||||
}
|
||||
ij++;
|
||||
}
|
||||
|
||||
if(a_norm != 0.0)
|
||||
{
|
||||
FT a_normEPS = a_norm * EPSILON;
|
||||
FT thr = a_norm;
|
||||
|
||||
// rotations
|
||||
int nb_iter = 0;
|
||||
while(thr > a_normEPS && nb_iter < MAX_ITER)
|
||||
{
|
||||
nb_iter++;
|
||||
FT thr_nn = thr / nn;
|
||||
|
||||
for(int l=1; l< n; l++)
|
||||
{
|
||||
for(int m=l+1; m<=n; m++)
|
||||
{
|
||||
// compute sinx and cosx
|
||||
int lq = (l*l-l)/2;
|
||||
int mq = (m*m-m)/2;
|
||||
|
||||
int lm = l + mq;
|
||||
FT a_lm = a[lm];
|
||||
FT a_lm_2 = a_lm * a_lm;
|
||||
|
||||
if(a_lm_2 < thr_nn)
|
||||
continue;
|
||||
|
||||
int ll = l + lq;
|
||||
int mm = m + mq;
|
||||
FT a_ll = a[ll];
|
||||
FT a_mm = a[mm];
|
||||
|
||||
FT delta = a_ll - a_mm;
|
||||
|
||||
FT x;
|
||||
if(delta == 0.0)
|
||||
x = (FT) - CGAL_PI / 4;
|
||||
else
|
||||
x = (FT)(- std::atan( (a_lm+a_lm) / delta ) / 2.0);
|
||||
|
||||
FT sinx = std::sin(x);
|
||||
FT cosx = std::cos(x);
|
||||
FT sinx_2 = sinx * sinx;
|
||||
FT cosx_2 = cosx * cosx;
|
||||
FT sincos = sinx * cosx;
|
||||
|
||||
// rotate L and M columns
|
||||
int ilv = n*(l-1);
|
||||
int imv = n*(m-1);
|
||||
|
||||
int i;
|
||||
for( i=1; i<=n;i++ )
|
||||
{
|
||||
if( (i!=l) && (i!=m) )
|
||||
{
|
||||
int iq = (i*i-i)/2;
|
||||
|
||||
int im;
|
||||
if( i<m )
|
||||
im = i + mq;
|
||||
else
|
||||
im = m + iq;
|
||||
FT a_im = a[im];
|
||||
|
||||
int il;
|
||||
if( i<l )
|
||||
il = i + lq;
|
||||
else
|
||||
il = l + iq;
|
||||
FT a_il = a[il];
|
||||
|
||||
a[il] = a_il * cosx - a_im * sinx;
|
||||
a[im] = a_il * sinx + a_im * cosx;
|
||||
}
|
||||
|
||||
ilv++;
|
||||
imv++;
|
||||
|
||||
FT v_ilv = v[ilv];
|
||||
FT v_imv = v[imv];
|
||||
|
||||
v[ilv] = cosx * v_ilv - sinx * v_imv;
|
||||
v[imv] = sinx * v_ilv + cosx * v_imv;
|
||||
}
|
||||
|
||||
x = a_lm * sincos;
|
||||
x += x;
|
||||
|
||||
a[ll] = a_ll * cosx_2 + a_mm * sinx_2 - x;
|
||||
a[mm] = a_ll * sinx_2 + a_mm * cosx_2 + x;
|
||||
a[lm] = 0.0;
|
||||
|
||||
thr = CGAL::abs(thr - a_lm_2);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// convert indices and copy eigen values
|
||||
a++;
|
||||
for(i=0; i<n; i++)
|
||||
{
|
||||
int k = i + (i*(i+1))/2;
|
||||
eigen_values[i] = a[k];
|
||||
}
|
||||
delete [] a;
|
||||
|
||||
// sort eigen values and vectors
|
||||
int *index = new int[n];
|
||||
for(i=0; i<n; i++)
|
||||
index[i] = i;
|
||||
|
||||
for(i=0; i<(n-1); i++)
|
||||
{
|
||||
FT x = eigen_values[i];
|
||||
int k = i;
|
||||
|
||||
for(int j=i+1; j<n; j++)
|
||||
if(x < eigen_values[j])
|
||||
{
|
||||
k = j;
|
||||
x = eigen_values[j];
|
||||
}
|
||||
|
||||
eigen_values[k] = eigen_values[i];
|
||||
eigen_values[i] = x;
|
||||
|
||||
int jj = index[k];
|
||||
index[k] = index[i];
|
||||
index[i] = jj;
|
||||
}
|
||||
|
||||
|
||||
// save eigen vectors
|
||||
v++; // back to C++
|
||||
ij = 0;
|
||||
for(int k=0; k<n; k++ )
|
||||
{
|
||||
int ik = index[k]*n;
|
||||
for(int i=0; i<n; i++)
|
||||
eigen_vectors[ij++] = v[ik++];
|
||||
}
|
||||
|
||||
delete [] v;
|
||||
delete [] index;
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} //namespace CGAL
|
||||
|
||||
#endif // CGAL_EIGEN_H
|
||||
|
|
@ -1,121 +0,0 @@
|
|||
// Copyright (c) 2005 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||||
// modify it under the terms of the GNU Lesser General Public License as
|
||||
// published by the Free Software Foundation; either version 3 of the License,
|
||||
// or (at your option) any later version.
|
||||
//
|
||||
// Licensees holding a valid commercial license may use this file in
|
||||
// accordance with the commercial license agreement provided with the software.
|
||||
//
|
||||
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||||
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||||
//
|
||||
// $URL$
|
||||
// $Id$
|
||||
//
|
||||
//
|
||||
// Author(s) : Pierre Alliez
|
||||
|
||||
#ifndef CGAL_EIGEN_2_H
|
||||
#define CGAL_EIGEN_2_H
|
||||
|
||||
#include <cmath>
|
||||
#include <utility>
|
||||
#include <CGAL/assertions.h>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
namespace internal {
|
||||
|
||||
// extract eigenvalues and eigenvectors from a 2x2 symmetric
|
||||
// positive definite matrix.
|
||||
// Note: computations involve a square root.
|
||||
// Matrix numbering:
|
||||
// a b
|
||||
// b c
|
||||
// Eigen values and vectors are sorted in descendent order.
|
||||
template <typename K>
|
||||
void eigen_symmetric_2(const typename K::FT *matrix, // a b c
|
||||
std::pair<typename K::Vector_2,
|
||||
typename K::Vector_2>& eigen_vectors,
|
||||
std::pair<typename K::FT,
|
||||
typename K::FT>& eigen_values)
|
||||
{
|
||||
// types
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Vector_2 Vector;
|
||||
|
||||
// for better reading
|
||||
FT a = matrix[0];
|
||||
FT b = matrix[1];
|
||||
FT c = matrix[2];
|
||||
FT p = c*c - 2*a*c + 4*b*b + a*a;
|
||||
CGAL_assertion(a >= 0.0 && c >= 0.0);
|
||||
|
||||
// degenerate or isotropic case
|
||||
if(p == 0.0)
|
||||
{
|
||||
// unit eigen values by default
|
||||
eigen_values.first = eigen_values.second = (FT)1.0;
|
||||
|
||||
// any vector is eigen vector
|
||||
// the 2D canonical frame is output by default
|
||||
eigen_vectors.first = Vector((FT)1.0,(FT)0.0);
|
||||
eigen_vectors.second = Vector((FT)0.0,(FT)1.0);
|
||||
}
|
||||
else
|
||||
{
|
||||
if(b == 0.0)
|
||||
{
|
||||
if(a>=c)
|
||||
{
|
||||
eigen_values.first = a;
|
||||
eigen_values.second = c;
|
||||
eigen_vectors.first = Vector((FT)1.0, (FT)0.0);
|
||||
eigen_vectors.second = Vector((FT)0.0, (FT)1.0);
|
||||
}
|
||||
else
|
||||
{
|
||||
eigen_values.first = c;
|
||||
eigen_values.second = a;
|
||||
eigen_vectors.first = Vector((FT)0.0, (FT)1.0);
|
||||
eigen_vectors.second = Vector((FT)1.0, (FT)0.0);
|
||||
}
|
||||
}
|
||||
else // generic case
|
||||
{
|
||||
FT l1 = (FT)(0.5 * ( -1*CGAL::sqrt(p) + c + a));
|
||||
FT l2 = (FT)(0.5 * ( CGAL::sqrt(p) + c + a));
|
||||
|
||||
// all eigen values of a symmetric positive
|
||||
// definite matrix must be real and positive
|
||||
// we saturate the values if this is not the
|
||||
// case for floating point computations.
|
||||
l1 = (l1 < (FT)0.0) ? (FT)0.0 : l1;
|
||||
l2 = (l2 < (FT)0.0) ? (FT)0.0 : l2;
|
||||
|
||||
// sort eigen values and vectors in descendent order.
|
||||
if(l1 >= l2)
|
||||
{
|
||||
eigen_values.first = l1;
|
||||
eigen_values.second = l2;
|
||||
eigen_vectors.first = Vector((FT)1.0, (FT)(-(CGAL::sqrt(p)-c+a) / (2*b)));
|
||||
eigen_vectors.second = Vector((FT)1.0, (FT)( (CGAL::sqrt(p)+c-a) / (2*b)));
|
||||
}
|
||||
else
|
||||
{
|
||||
eigen_values.first = l2;
|
||||
eigen_values.second = l1;
|
||||
eigen_vectors.first = Vector((FT)1.0, (FT)( (CGAL::sqrt(p)+c-a) / (2*b)));
|
||||
eigen_vectors.second = Vector((FT)1.0, (FT)(-(CGAL::sqrt(p)-c+a) / (2*b)));
|
||||
}
|
||||
} // end generic case
|
||||
} // end non-degenerate case
|
||||
} // end eigen_symmetric_2
|
||||
} // end namespace internal
|
||||
|
||||
} //namespace CGAL
|
||||
|
||||
#endif // CGAL_EIGEN_2_H
|
||||
|
|
@ -29,14 +29,15 @@
|
|||
#include <CGAL/linear_least_squares_fitting_circles_2.h>
|
||||
#include <CGAL/linear_least_squares_fitting_rectangles_2.h>
|
||||
#include <CGAL/Dimension.h>
|
||||
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
#include <iterator>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
template < typename InputIterator,
|
||||
typename Kernel,
|
||||
typename Tag>
|
||||
typename Tag,
|
||||
typename Diagonalize_traits>
|
||||
inline
|
||||
typename Kernel::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
|
|
@ -44,35 +45,39 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename Kernel::Line_2& line,
|
||||
typename Kernel::Point_2& centroid,
|
||||
const Tag& tag,
|
||||
const Kernel& kernel)
|
||||
const Kernel& kernel,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
|
||||
return internal::linear_least_squares_fitting_2(first, beyond, line,
|
||||
centroid,(Value_type*)NULL,kernel,tag);
|
||||
centroid,(Value_type*)NULL,kernel,tag,
|
||||
diagonalize_traits);
|
||||
}
|
||||
|
||||
// deduces the kernel from the points in container.
|
||||
// Use default Diagonalize_traits
|
||||
template < typename InputIterator,
|
||||
typename Line,
|
||||
typename Point,
|
||||
typename Tag>
|
||||
typename Tag>
|
||||
inline
|
||||
typename Kernel_traits<Line>::Kernel::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
Line& line,
|
||||
Point& centroid,
|
||||
const Tag& tag)
|
||||
const Tag& tag)
|
||||
{
|
||||
typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
|
||||
typedef typename Kernel_traits<Value_type>::Kernel Kernel;
|
||||
return CGAL::linear_least_squares_fitting_2(first,beyond,line,centroid,tag,Kernel());
|
||||
return CGAL::linear_least_squares_fitting_2
|
||||
(first,beyond,line,centroid,tag,Kernel(),
|
||||
Default_diagonalize_traits<typename Kernel::FT, 2>());
|
||||
}
|
||||
|
||||
|
||||
template < typename InputIterator,
|
||||
typename Line,
|
||||
typename Tag >
|
||||
typename Tag>
|
||||
inline
|
||||
typename Kernel_traits<Line>::Kernel::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
|
|
@ -83,7 +88,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
|
||||
typedef typename Kernel_traits<Value_type>::Kernel Kernel;
|
||||
typename Kernel::Point_2 centroid; // unused
|
||||
return CGAL::linear_least_squares_fitting_2(first,beyond,line,centroid,tag,Kernel());
|
||||
return CGAL::linear_least_squares_fitting_2(first,beyond,line,centroid,tag,Kernel(),
|
||||
Default_diagonalize_traits<typename Kernel::FT, 2>());
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -21,8 +21,6 @@
|
|||
#define CGAL_LINEAR_LEAST_SQUARES_FITTING_3_H
|
||||
|
||||
#include <CGAL/basic.h>
|
||||
//#include <CGAL/Algebraic_structure_traits.h>
|
||||
//#include <CGAL/IO/io.h>
|
||||
|
||||
#include <CGAL/linear_least_squares_fitting_points_3.h>
|
||||
#include <CGAL/linear_least_squares_fitting_segments_3.h>
|
||||
|
|
@ -31,6 +29,8 @@
|
|||
#include <CGAL/linear_least_squares_fitting_tetrahedra_3.h>
|
||||
#include <CGAL/linear_least_squares_fitting_spheres_3.h>
|
||||
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <CGAL/Dimension.h>
|
||||
|
||||
#include <iterator>
|
||||
|
|
@ -42,7 +42,8 @@ namespace CGAL {
|
|||
template < typename InputIterator,
|
||||
typename Object,
|
||||
typename Kernel,
|
||||
typename Tag >
|
||||
typename Tag,
|
||||
typename Diagonalize_traits >
|
||||
inline
|
||||
typename Kernel::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
|
|
@ -50,32 +51,38 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
Object& object, // plane or line
|
||||
typename Kernel::Point_3& centroid,
|
||||
const Tag& tag, // dimension tag, ranges from 0 to 3
|
||||
const Kernel& kernel)
|
||||
const Kernel& kernel,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
|
||||
return internal::linear_least_squares_fitting_3(first, beyond, object,
|
||||
centroid, (Value_type*) NULL, kernel, tag);
|
||||
centroid, (Value_type*) NULL, kernel, tag,
|
||||
diagonalize_traits);
|
||||
}
|
||||
|
||||
// deduces kernel from value type of input iterator
|
||||
// use default Diagonalize_traits
|
||||
template < typename InputIterator,
|
||||
typename Object,
|
||||
typename Point,
|
||||
typename Tag>
|
||||
typename Point,
|
||||
typename Tag >
|
||||
inline
|
||||
typename Kernel_traits<Object>::Kernel::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
Object& object, // plane or line
|
||||
Point& centroid,
|
||||
const Tag& tag) // dimension tag, ranges from 0 to 3
|
||||
const Tag& tag) // dimension tag, ranges from 0 to 3
|
||||
{
|
||||
typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
|
||||
typedef typename Kernel_traits<Value_type>::Kernel Kernel;
|
||||
return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag,Kernel());
|
||||
return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag,Kernel(),
|
||||
Default_diagonalize_traits<typename Kernel::FT, 3>());
|
||||
|
||||
}
|
||||
|
||||
// deduces kernel and does not write centroid
|
||||
// use default Diagonalize_traits
|
||||
template < typename InputIterator,
|
||||
typename Object,
|
||||
typename Tag>
|
||||
|
|
@ -84,12 +91,14 @@ typename Kernel_traits<Object>::Kernel::FT
|
|||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
Object& object, // plane or line
|
||||
const Tag& tag) // dimension tag, ranges from 0 to 3
|
||||
const Tag& tag) // dimension tag, ranges from 0 to 3
|
||||
{
|
||||
typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
|
||||
typedef typename Kernel_traits<Value_type>::Kernel Kernel;
|
||||
typename Kernel::Point_3 centroid; // not used by caller
|
||||
return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag);
|
||||
return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag,Kernel(),
|
||||
Default_diagonalize_traits<typename Kernel::FT, 3>());
|
||||
|
||||
}
|
||||
|
||||
} //namespace CGAL
|
||||
|
|
|
|||
|
|
@ -22,8 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen_2.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/Linear_algebraCd.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
|
|
@ -40,7 +38,7 @@ namespace internal {
|
|||
// 0 is worst (isotropic case, returns a line with horizontal
|
||||
// direction by default)
|
||||
|
||||
template < typename InputIterator, typename K >
|
||||
template < typename InputIterator, typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -48,7 +46,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Circle_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits&)
|
||||
{
|
||||
// types
|
||||
typedef typename K::FT FT;
|
||||
|
|
@ -67,11 +66,11 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 0 1
|
||||
// 2
|
||||
//Final combined covariance matrix for all circles and their combined mass
|
||||
FT mass = 0.0;
|
||||
FT covariance[3] = {0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 3> covariance = {{ 0., 0., 0. }};
|
||||
|
||||
// assemble 2nd order moment about the origin.
|
||||
FT temp[4] = {0.25, 0.0,
|
||||
|
|
@ -120,22 +119,19 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
std::pair<FT,FT> eigen_values;
|
||||
std::pair<Vector,Vector> eigen_vectors;
|
||||
// internal::eigen_symmetric_2<K>(final_cov, eigen_vectors, eigen_values);
|
||||
FT eigen_vectors1[4];
|
||||
FT eigen_values1[2];
|
||||
eigen_symmetric<FT>(covariance,2, eigen_vectors1, eigen_values1);
|
||||
eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
|
||||
eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
|
||||
CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
|
||||
CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// check unicity and build fitting line accordingly
|
||||
if(eigen_values.first != eigen_values.second)
|
||||
if(eigen_values[0] != eigen_values[1])
|
||||
{
|
||||
// regular case
|
||||
line = Line(c, eigen_vectors.first);
|
||||
return (FT)1.0 - eigen_values.second / eigen_values.first;
|
||||
line = Line(c, Vector (eigen_vectors[2],eigen_vectors[3]));
|
||||
return (FT)1.0 - eigen_values[0] / eigen_values[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
|
|
@ -148,7 +144,7 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
|
||||
} // end linear_least_squares_fitting_2 for circle set with 2D tag
|
||||
|
||||
template < typename InputIterator, typename K >
|
||||
template < typename InputIterator, typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -156,7 +152,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Circle_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& )
|
||||
{
|
||||
// types
|
||||
typedef typename K::FT FT;
|
||||
|
|
@ -174,11 +171,11 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
// 0 1
|
||||
// 2
|
||||
//Final combined covariance matrix for all circles and their combined mass
|
||||
FT mass = 0.0;
|
||||
FT covariance[3] = {0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 3> covariance = {{ 0., 0., 0. }};
|
||||
|
||||
// assemble 2nd order moment about the origin.
|
||||
FT temp[4] = {1.0, 0.0,
|
||||
|
|
@ -226,22 +223,19 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
std::pair<FT,FT> eigen_values;
|
||||
std::pair<Vector,Vector> eigen_vectors;
|
||||
// internal::eigen_symmetric_2<K>(final_cov, eigen_vectors, eigen_values);
|
||||
FT eigen_vectors1[4];
|
||||
FT eigen_values1[2];
|
||||
eigen_symmetric<FT>(covariance,2, eigen_vectors1, eigen_values1);
|
||||
eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
|
||||
eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
|
||||
CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
|
||||
CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// check unicity and build fitting line accordingly
|
||||
if(eigen_values.first != eigen_values.second)
|
||||
if(eigen_values[1] != eigen_values[0])
|
||||
{
|
||||
// regular case
|
||||
line = Line(c, eigen_vectors.first);
|
||||
return (FT)1.0 - eigen_values.second / eigen_values.first;
|
||||
line = Line(c, Vector(eigen_vectors[2],eigen_vectors[3]));
|
||||
return (FT)1.0 - eigen_values[0] / eigen_values[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
|
|
|
|||
|
|
@ -22,7 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
#include <CGAL/linear_least_squares_fitting_points_3.h>
|
||||
#include <CGAL/linear_least_squares_fitting_segments_3.h>
|
||||
|
|
@ -36,7 +35,8 @@ namespace internal {
|
|||
|
||||
// fits a plane to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -44,7 +44,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<3>& tag)
|
||||
const CGAL::Dimension_tag<3>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -56,18 +57,19 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,k,tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a plane to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -75,7 +77,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -87,18 +90,19 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,k,tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a plane to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -106,7 +110,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Segment_3 Segment;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -135,13 +140,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a plane to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -149,7 +156,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Point_3 Point;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -174,13 +182,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a line to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -188,7 +198,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<3>& tag)
|
||||
const CGAL::Dimension_tag<3>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -200,17 +211,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,k,tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a line to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -218,7 +230,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -230,18 +243,19 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,k,tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a line to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -249,7 +263,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Segment_3 Segment;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -278,13 +293,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
// fits a line to a 3D cuboid set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -292,7 +309,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Iso_cuboid_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Point_3 Point;
|
||||
typedef typename K::Iso_cuboid_3 Iso_cuboid;
|
||||
|
|
@ -317,7 +335,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_cuboids_3
|
||||
|
||||
|
|
|
|||
|
|
@ -22,8 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen_2.h>
|
||||
|
||||
#include <iterator>
|
||||
#include <cmath>
|
||||
|
||||
|
|
@ -37,7 +35,8 @@ namespace internal {
|
|||
// 0 is worst (isotropic case, returns a line with horizontal
|
||||
// direction by default).
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits>
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -45,7 +44,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Point_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits&)
|
||||
{
|
||||
// types
|
||||
typedef typename K::FT FT;
|
||||
|
|
@ -63,9 +63,11 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
|
||||
// assemble covariance matrix as a semi-definite matrix.
|
||||
// Matrix numbering:
|
||||
// 0
|
||||
// 1 2
|
||||
FT covariance[3] = {0,0,0};
|
||||
// 0 1
|
||||
// 2
|
||||
|
||||
CGAL::cpp11::array<FT, 3> covariance = {{ 0., 0., 0. }};
|
||||
|
||||
for(InputIterator it = first;
|
||||
it != beyond;
|
||||
it++)
|
||||
|
|
@ -78,18 +80,19 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
}
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
std::pair<FT,FT> eigen_values;
|
||||
std::pair<Vector,Vector> eigen_vectors;
|
||||
internal::eigen_symmetric_2<K>(covariance, eigen_vectors, eigen_values);
|
||||
CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
|
||||
CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// check unicity and build fitting line accordingly
|
||||
if(eigen_values.first != eigen_values.second)
|
||||
if(eigen_values[0] != eigen_values[1])
|
||||
{
|
||||
// regular case
|
||||
line = Line(c, eigen_vectors.first);
|
||||
return (FT)1.0 - eigen_values.second / eigen_values.first;
|
||||
line = Line(c, Vector (eigen_vectors[2], eigen_vectors[3]));
|
||||
return (FT)1.0 - eigen_values[0] / eigen_values[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
|
|
|
|||
|
|
@ -22,7 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
#include <iterator>
|
||||
|
|
@ -35,7 +34,8 @@ namespace internal {
|
|||
// 1 is best (zero variance orthogonally to the fitting line)
|
||||
// 0 is worst (isotropic case, returns a plane with default direction)
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -43,7 +43,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Point_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -55,11 +56,11 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6];
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Point*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
} // end fit plane to point set
|
||||
|
||||
// fits a line to a 3D point set
|
||||
|
|
@ -67,7 +68,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
// 1 is best (zero variance orthogonally to the fitting line)
|
||||
// 0 is worst (isotropic case, returns a line along x axis)
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -75,7 +77,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Point_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -87,11 +90,11 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6];
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Point*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
} // end fit line to point set
|
||||
|
||||
} // end namespace internal
|
||||
|
|
|
|||
|
|
@ -22,8 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen_2.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/Linear_algebraCd.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
|
|
@ -40,7 +38,7 @@ namespace internal {
|
|||
// 0 is worst (isotropic case, returns a line with horizontal
|
||||
// direction by default)
|
||||
|
||||
template < typename InputIterator, typename K >
|
||||
template < typename InputIterator, typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -48,7 +46,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Iso_rectangle_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits&)
|
||||
{
|
||||
// types
|
||||
typedef typename K::FT FT;
|
||||
|
|
@ -70,7 +69,7 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
// 1 2
|
||||
//Final combined covariance matrix for all rectangles and their combined mass
|
||||
FT mass = 0.0;
|
||||
FT covariance[3] = {0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 3> covariance = {{ 0., 0., 0. }};
|
||||
|
||||
// assemble 2nd order moment about the origin.
|
||||
FT temp[4] = {1/3.0, 0.25,
|
||||
|
|
@ -123,22 +122,19 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
std::pair<FT,FT> eigen_values;
|
||||
std::pair<Vector,Vector> eigen_vectors;
|
||||
FT eigen_vectors1[4];
|
||||
FT eigen_values1[2];
|
||||
eigen_symmetric<FT>(covariance,2, eigen_vectors1, eigen_values1);
|
||||
eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
|
||||
eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
|
||||
CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
|
||||
CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// check unicity and build fitting line accordingly
|
||||
if(eigen_values.first != eigen_values.second)
|
||||
if(eigen_values[0] != eigen_values[1])
|
||||
{
|
||||
// regular case
|
||||
line = Line(c, eigen_vectors.first);
|
||||
return (FT)1.0 - eigen_values.second / eigen_values.first;
|
||||
line = Line(c, Vector(eigen_vectors[2],eigen_vectors[3]));
|
||||
return (FT)1.0 - eigen_values[0] / eigen_values[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
|
|
@ -150,7 +146,7 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
}
|
||||
} // end linear_least_squares_fitting_2 for rectangle set with 2D tag
|
||||
|
||||
template < typename InputIterator, typename K >
|
||||
template < typename InputIterator, typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -158,7 +154,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Iso_rectangle_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
// types
|
||||
typedef typename K::Iso_rectangle_2 Iso_rectangle;
|
||||
|
|
@ -179,13 +176,15 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
segments.push_back(Segment_2(t[3],t[0]));
|
||||
}
|
||||
|
||||
return linear_least_squares_fitting_2(segments.begin(),segments.end(),line,c,K(),tag);
|
||||
return linear_least_squares_fitting_2(segments.begin(),segments.end(),line,c,K(),tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_2 for rectangle set with 1D tag
|
||||
|
||||
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -193,7 +192,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Iso_rectangle_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
// types
|
||||
typedef typename K::Iso_rectangle_2 Iso_rectangle;
|
||||
|
|
@ -214,7 +214,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
points.push_back(Point_2(t[3]));
|
||||
}
|
||||
|
||||
return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,K(),tag);
|
||||
return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,K(),tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_2 for rectangle set with 0D tag
|
||||
|
||||
|
|
|
|||
|
|
@ -22,8 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen_2.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/Linear_algebraCd.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
|
|
@ -40,7 +38,7 @@ namespace internal {
|
|||
// 0 is worst (isotropic case, returns a line with horizontal
|
||||
// direction by default)
|
||||
|
||||
template < typename InputIterator, typename K >
|
||||
template < typename InputIterator, typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -48,7 +46,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Segment_2*,// used for indirection
|
||||
const K&, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag = CGAL::Dimension_tag<1>())
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits&)
|
||||
{
|
||||
// types
|
||||
typedef typename K::FT FT;
|
||||
|
|
@ -69,7 +68,7 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
// 1 2
|
||||
//Final combined covariance matrix for all segments and their combined mass
|
||||
FT mass = 0.0;
|
||||
FT covariance[3] = {0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 3> covariance = {{ 0., 0., 0. }};
|
||||
|
||||
// assemble 2nd order moment about the origin.
|
||||
FT temp[4] = {1.0, 0.5, 0.5, 1.0};
|
||||
|
|
@ -111,22 +110,19 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
covariance[2] += mass * (-1.0 * c.y() * c.y());
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
std::pair<FT,FT> eigen_values;
|
||||
std::pair<Vector,Vector> eigen_vectors;
|
||||
// internal::eigen_symmetric_2<K>(covariance, eigen_vectors, eigen_values);
|
||||
FT eigen_vectors1[4];
|
||||
FT eigen_values1[2];
|
||||
eigen_symmetric<FT>(covariance,2, eigen_vectors1, eigen_values1);
|
||||
eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
|
||||
eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
|
||||
CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
|
||||
CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// check unicity and build fitting line accordingly
|
||||
if(eigen_values.first != eigen_values.second)
|
||||
if(eigen_values[0] != eigen_values[1])
|
||||
{
|
||||
// regular case
|
||||
line = Line(c, eigen_vectors.first);
|
||||
return (FT)1.0 - eigen_values.second / eigen_values.first;
|
||||
line = Line(c, Vector(eigen_vectors[2],eigen_vectors[3]));
|
||||
return (FT)1.0 - eigen_values[0] / eigen_values[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
|
|
@ -138,7 +134,7 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
}
|
||||
} // end linear_least_squares_fitting_2 for segment set with 1D tag
|
||||
|
||||
template < typename InputIterator, typename K >
|
||||
template < typename InputIterator, typename K, typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -146,7 +142,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename K::Point_2& c, // centroid
|
||||
const typename K::Segment_2*,// used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
// types
|
||||
typedef typename K::Point_2 Point;
|
||||
|
|
@ -164,7 +161,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
points.push_back(s[0]);
|
||||
points.push_back(s[1]);
|
||||
}
|
||||
return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,k,(Point*)NULL,tag);
|
||||
return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,k,(Point*)NULL,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_2 for segment set with 1D tag
|
||||
|
||||
|
|
|
|||
|
|
@ -22,7 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
#include <CGAL/linear_least_squares_fitting_points_3.h>
|
||||
|
||||
|
|
@ -35,7 +34,8 @@ namespace internal {
|
|||
|
||||
// fits a plane to a 3D segment set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -43,7 +43,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Segment_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Segment_3 Segment;
|
||||
|
|
@ -55,17 +56,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,k,tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Segment*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_segments_3
|
||||
|
||||
// fits a plane to a 3D segment set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -73,7 +75,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Segment_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Segment_3 Segment;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -92,13 +95,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_segments_3
|
||||
|
||||
// fits a line to a 3D segment set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -106,7 +111,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Segment_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Segment_3 Segment;
|
||||
|
|
@ -118,17 +124,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,k,tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Segment*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_segments_3
|
||||
|
||||
// fits a plane to a 3D segment set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -136,7 +143,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Segment_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Segment_3 Segment;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -155,7 +163,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_segments_3
|
||||
|
||||
|
|
|
|||
|
|
@ -22,7 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
#include <iterator>
|
||||
|
|
@ -33,7 +32,8 @@ namespace internal {
|
|||
|
||||
// fits a plane to a set of 3D balls (3D)
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -41,7 +41,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Sphere_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<3>& tag)
|
||||
const CGAL::Dimension_tag<3>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Sphere_3 Sphere;
|
||||
|
|
@ -53,17 +54,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_spheres_3
|
||||
|
||||
// fits a plane to a 3D sphere set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -71,7 +73,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Sphere_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Sphere_3 Sphere;
|
||||
|
|
@ -83,18 +86,19 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_spheres_3
|
||||
|
||||
|
||||
// fits a line to a 3D ball set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -102,7 +106,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Sphere_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<3>& tag)
|
||||
const CGAL::Dimension_tag<3>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Sphere_3 Sphere;
|
||||
|
|
@ -114,18 +119,19 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
|
||||
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_spheres_3
|
||||
|
||||
// fits a line to a 3D sphere set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -133,7 +139,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Sphere_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Sphere_3 Sphere;
|
||||
|
|
@ -145,11 +152,11 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_spheres_3
|
||||
|
||||
|
|
|
|||
|
|
@ -22,7 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen.h>
|
||||
|
||||
#include <CGAL/PCA_util.h>
|
||||
#include <CGAL/linear_least_squares_fitting_points_3.h>
|
||||
|
|
@ -37,7 +36,8 @@ namespace internal {
|
|||
|
||||
// fits a plane to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -45,7 +45,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<3>& tag)
|
||||
const CGAL::Dimension_tag<3>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
|
|
@ -57,16 +58,17 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Tetrahedron*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a plane to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -74,7 +76,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
|
|
@ -95,13 +98,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(triangles.begin(),triangles.end(),plane,c,(Triangle*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(triangles.begin(),triangles.end(),plane,c,(Triangle*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a plane to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -109,7 +114,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
typedef typename K::Segment_3 Segment;
|
||||
|
|
@ -133,13 +139,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a plane to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -147,7 +155,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -168,13 +177,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a line to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -182,7 +193,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<3>& tag)
|
||||
const CGAL::Dimension_tag<3>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
|
|
@ -194,17 +206,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Tetrahedron*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a line to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -212,7 +225,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
|
|
@ -233,13 +247,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(triangles.begin(),triangles.end(),line,c,(Triangle*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(triangles.begin(),triangles.end(),line,c,(Triangle*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a line to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -247,7 +263,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
typedef typename K::Segment_3 Segment;
|
||||
|
|
@ -270,13 +287,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedrons_3
|
||||
|
||||
// fits a line to a 3D tetrahedron set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -284,7 +303,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Tetrahedron_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Tetrahedron_3 Tetrahedron;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -305,7 +325,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_tetrahedra_3
|
||||
|
||||
|
|
|
|||
|
|
@ -22,8 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen_2.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/Linear_algebraCd.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
|
|
@ -41,7 +39,7 @@ namespace internal {
|
|||
// direction by default)
|
||||
|
||||
template < typename InputIterator,
|
||||
typename Kernel >
|
||||
typename Kernel, typename Diagonalize_traits >
|
||||
typename Kernel::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -49,7 +47,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename Kernel::Point_2& c, // centroid
|
||||
const typename Kernel::Triangle_2*,// used for indirection
|
||||
const Kernel&, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits&)
|
||||
{
|
||||
// types
|
||||
typedef typename Kernel::FT FT;
|
||||
|
|
@ -71,7 +70,7 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
// 1 2
|
||||
//Final combined covariance matrix for all triangles and their combined mass
|
||||
FT mass = 0.0;
|
||||
FT covariance[3] = {0.0, 0.0, 0.0};
|
||||
CGAL::cpp11::array<FT, 3> covariance = {{ 0., 0., 0. }};
|
||||
|
||||
// assemble the 2nd order moment about the origin.
|
||||
FT temp[4] = {1/12.0, 1/24.0,
|
||||
|
|
@ -123,21 +122,19 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
// std::cout<<"cov: "<<covariance[0]*covariance[2]<<" =? "<<covariance[1]*covariance[1]<<std::endl;
|
||||
|
||||
// solve for eigenvalues and eigenvectors.
|
||||
// eigen values are sorted in descending order,
|
||||
// eigen values are sorted in ascending order,
|
||||
// eigen vectors are sorted in accordance.
|
||||
std::pair<FT,FT> eigen_values;
|
||||
std::pair<Vector,Vector> eigen_vectors;
|
||||
FT eigen_vectors1[4];
|
||||
FT eigen_values1[2];
|
||||
eigen_symmetric<FT>(covariance,2, eigen_vectors1, eigen_values1);
|
||||
eigen_values = std::make_pair(eigen_values1[0],eigen_values1[1]);
|
||||
eigen_vectors = std::make_pair(Vector(eigen_vectors1[0],eigen_vectors1[1]),Vector(eigen_vectors1[2],eigen_vectors1[3]));
|
||||
CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
|
||||
CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
|
||||
Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigen_values, eigen_vectors);
|
||||
|
||||
// check unicity and build fitting line accordingly
|
||||
if(eigen_values.first != eigen_values.second)
|
||||
if(eigen_values[0] != eigen_values[1])
|
||||
{
|
||||
// regular case
|
||||
line = Line(c, eigen_vectors.first);
|
||||
return (FT)1.0 - eigen_values.second / eigen_values.first;
|
||||
line = Line(c, Vector(eigen_vectors[2],eigen_vectors[3]));
|
||||
return (FT)1.0 - eigen_values[0] / eigen_values[1];
|
||||
}
|
||||
else
|
||||
{
|
||||
|
|
@ -150,7 +147,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
} // end linear_least_squares_fitting_2 for triangle set with 2D tag
|
||||
|
||||
template < typename InputIterator,
|
||||
typename Kernel >
|
||||
typename Kernel,
|
||||
typename Diagonalize_traits >
|
||||
typename Kernel::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -158,7 +156,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename Kernel::Point_2& c, // centroid
|
||||
const typename Kernel::Triangle_2*,// used for indirection
|
||||
const Kernel&, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
// types
|
||||
typedef typename Kernel::Triangle_2 Triangle;
|
||||
|
|
@ -178,12 +177,14 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
segments.push_back(Segment(t[2],t[0]));
|
||||
}
|
||||
|
||||
return linear_least_squares_fitting_2(segments.begin(),segments.end(),line,c,tag,Kernel());
|
||||
return linear_least_squares_fitting_2(segments.begin(),segments.end(),line,c,tag,Kernel(),
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_2 for triangle set with 1D tag
|
||||
|
||||
template < typename InputIterator,
|
||||
typename Kernel >
|
||||
typename Kernel,
|
||||
typename Diagonalize_traits >
|
||||
typename Kernel::FT
|
||||
linear_least_squares_fitting_2(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -191,7 +192,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
typename Kernel::Point_2& c, // centroid
|
||||
const typename Kernel::Triangle_2*,// used for indirection
|
||||
const Kernel&, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
// types
|
||||
|
||||
|
|
@ -212,7 +214,8 @@ linear_least_squares_fitting_2(InputIterator first,
|
|||
points.push_back(Point(t[2]));
|
||||
}
|
||||
|
||||
return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,tag,Kernel());
|
||||
return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,tag,Kernel(),
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_2 for triangle set with 0D tag
|
||||
|
||||
|
|
|
|||
|
|
@ -22,7 +22,6 @@
|
|||
|
||||
#include <CGAL/basic.h>
|
||||
#include <CGAL/centroid.h>
|
||||
#include <CGAL/eigen.h>
|
||||
#include <CGAL/PCA_util.h>
|
||||
|
||||
#include <list>
|
||||
|
|
@ -34,7 +33,8 @@ namespace internal {
|
|||
|
||||
// fits a plane to a 3D triangle set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -42,7 +42,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Triangle_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
|
|
@ -54,17 +55,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Triangle*) NULL,tag);
|
||||
|
||||
// compute fitting plane
|
||||
return fitting_plane_3(covariance,c,plane,k);
|
||||
return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_triangles_3
|
||||
|
||||
// fits a plane to a 3D triangle set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -72,7 +74,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Triangle_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
typedef typename K::Segment_3 Segment;
|
||||
|
|
@ -92,13 +95,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_triangles_3
|
||||
|
||||
// fits a plane to a 3D triangle set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -106,7 +111,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Triangle_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -125,13 +131,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting plane
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_triangles_3
|
||||
|
||||
// fits a line to a 3D triangle set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -139,7 +147,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Triangle_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<2>& tag)
|
||||
const CGAL::Dimension_tag<2>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::FT FT;
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
|
|
@ -151,17 +160,18 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
c = centroid(first,beyond,K(),tag);
|
||||
|
||||
// assemble covariance matrix
|
||||
FT covariance[6] = {0.0,0.0,0.0,0.0,0.0,0.0};
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Triangle*) NULL,tag);
|
||||
|
||||
// compute fitting line
|
||||
return fitting_line_3(covariance,c,line,k);
|
||||
return fitting_line_3(covariance,c,line,k,diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_triangles_3
|
||||
|
||||
// fits a line to a 3D triangle set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -169,7 +179,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Triangle_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<1>& tag)
|
||||
const CGAL::Dimension_tag<1>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
typedef typename K::Segment_3 Segment;
|
||||
|
|
@ -189,13 +200,15 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_triangles_3
|
||||
|
||||
// fits a line to a 3D triangle set
|
||||
template < typename InputIterator,
|
||||
typename K >
|
||||
typename K,
|
||||
typename Diagonalize_traits >
|
||||
typename K::FT
|
||||
linear_least_squares_fitting_3(InputIterator first,
|
||||
InputIterator beyond,
|
||||
|
|
@ -203,7 +216,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
typename K::Point_3& c, // centroid
|
||||
const typename K::Triangle_3*, // used for indirection
|
||||
const K& k, // kernel
|
||||
const CGAL::Dimension_tag<0>& tag)
|
||||
const CGAL::Dimension_tag<0>& tag,
|
||||
const Diagonalize_traits& diagonalize_traits)
|
||||
{
|
||||
typedef typename K::Triangle_3 Triangle;
|
||||
typedef typename K::Point_3 Point;
|
||||
|
|
@ -222,7 +236,8 @@ linear_least_squares_fitting_3(InputIterator first,
|
|||
}
|
||||
|
||||
// compute fitting line
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag);
|
||||
return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
|
||||
diagonalize_traits);
|
||||
|
||||
} // end linear_least_squares_fitting_triangles_3
|
||||
|
||||
|
|
|
|||
|
|
@ -3,6 +3,7 @@
|
|||
#include <CGAL/algorithm.h>
|
||||
#include <CGAL/linear_least_squares_fitting_2.h>
|
||||
#include <CGAL/point_generators_2.h>
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <vector>
|
||||
#include <cassert>
|
||||
|
|
@ -31,7 +32,9 @@ void test_2D()
|
|||
FT quality;
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),k);
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),k,
|
||||
CGAL::Default_diagonalize_traits<FT,2>());
|
||||
|
||||
std::cout << "done (quality: " << quality << ")" << std::endl;
|
||||
|
||||
if(!line.is_horizontal())
|
||||
|
|
@ -71,7 +74,8 @@ void test_2D_point_set(const unsigned int nb_points)
|
|||
FT quality;
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),k);
|
||||
quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),k,
|
||||
CGAL::Default_diagonalize_traits<FT,2>());
|
||||
|
||||
std::cout << "done (quality: " << quality << ")" << std::endl;
|
||||
|
||||
|
|
|
|||
|
|
@ -3,6 +3,8 @@
|
|||
|
||||
#include <CGAL/Cartesian.h>
|
||||
#include <CGAL/linear_least_squares_fitting_3.h>
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <cassert>
|
||||
|
||||
#include <cstdlib>
|
||||
|
|
@ -43,13 +45,17 @@ void fit_point_set(std::list<Point>& points,
|
|||
std::cout << "fit 3D line...";
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),kernel);
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
|
||||
std::cout << "done (quality: " << quality << ")" << std::endl;
|
||||
|
||||
std::cout << "fit 3D plane...";
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>());
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>(),kernel);
|
||||
quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
|
||||
std::cout << "done (quality: " << quality << ")" << std::endl;
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@
|
|||
#include <CGAL/algorithm.h>
|
||||
#include <CGAL/linear_least_squares_fitting_3.h>
|
||||
#include <CGAL/point_generators_3.h>
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <vector>
|
||||
#include <cassert>
|
||||
|
|
@ -34,13 +35,15 @@ FT fit_set(std::list<Segment>& segments,
|
|||
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),line,CGAL::Dimension_tag<1>());
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),line,centroid,CGAL::Dimension_tag<1>());
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),line,centroid,CGAL::Dimension_tag<1>(),kernel);
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),line,centroid,CGAL::Dimension_tag<1>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,CGAL::Dimension_tag<1>());
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,centroid,CGAL::Dimension_tag<1>());
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,centroid,CGAL::Dimension_tag<1>(),kernel);
|
||||
quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,centroid,CGAL::Dimension_tag<1>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
|
||||
return quality;
|
||||
return quality;
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -2,6 +2,7 @@
|
|||
|
||||
#include <CGAL/Cartesian.h>
|
||||
#include <CGAL/linear_least_squares_fitting_3.h>
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <list>
|
||||
|
||||
|
|
@ -34,19 +35,23 @@ int main(void)
|
|||
Kernel kernel;
|
||||
Point centroid;
|
||||
|
||||
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::Dimension_tag<3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::Dimension_tag<2>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>(),kernel);
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>(),kernel);
|
||||
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,CGAL::Dimension_tag<3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,CGAL::Dimension_tag<2>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>(),kernel);
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>(),kernel);
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>(),kernel,
|
||||
CGAL::Default_diagonalize_traits<FT,3>());
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
|
|||
|
|
@ -15,7 +15,7 @@
|
|||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.3}
|
||||
\cgalPkgDependsOn{ \ref PkgJet_fitting_3Summary and solvers from \ref thirdpartyEigen.}
|
||||
\cgalPkgDependsOn{\ref PkgSolverSummary}
|
||||
\cgalPkgBib{cgal:cp-arutsm}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgShortInfoEnd
|
||||
|
|
|
|||
|
|
@ -1,136 +0,0 @@
|
|||
//Orthogonal projection of a point onto a weighted PCA plane.
|
||||
//Copyright (C) 2014 INRIA - Sophia Antipolis
|
||||
//
|
||||
//This program is free software: you can redistribute it and/or modify
|
||||
//it under the terms of the GNU General Public License as published by
|
||||
//the Free Software Foundation, either version 3 of the License, or
|
||||
//(at your option) any later version.
|
||||
//
|
||||
//This program is distributed in the hope that it will be useful,
|
||||
//but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
//MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
//GNU General Public License for more details.
|
||||
//
|
||||
//You should have received a copy of the GNU General Public License
|
||||
//along with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||
//
|
||||
// Author(s): Thijs van Lankveld
|
||||
|
||||
|
||||
/// A concept for computing an approximation of a weighted point set.
|
||||
/** \ingroup PkgScaleSpaceReconstruction3Concepts
|
||||
* \cgalConcept
|
||||
* This approximation can be used to fit other points to the point set.
|
||||
*
|
||||
* \cgalHasModel `CGAL::Weighted_PCA_approximation_3`
|
||||
*/
|
||||
class WeightedApproximation_3 {
|
||||
public:
|
||||
/// \name Types
|
||||
/// \{
|
||||
typedef unspecified_type FT; ///< defines the field number type.
|
||||
typedef unspecified_type Point; ///< defines the point type.
|
||||
|
||||
/// \}
|
||||
|
||||
public:
|
||||
/// \name Constructors
|
||||
/// \{
|
||||
/// constructs an approximation of a undefined point set.
|
||||
/** The point set holds a fixed number of points with undefined coordinates.
|
||||
*
|
||||
* \param size is the size of the points set.
|
||||
*
|
||||
* \note this does not compute the approximation.
|
||||
*/
|
||||
WeightedApproximation_3( unsigned int size );
|
||||
|
||||
/// \}
|
||||
|
||||
// computes the approximation of a point set.
|
||||
/* Similar to constructing a approximation and calling
|
||||
* <code>[set_points(points_begin, points_end, weights_begin)](\ref WeightedApproximation_3::set_points )</code>
|
||||
*
|
||||
* \tparam PointIterator is an input iterator over the point collection.
|
||||
* The value type of the iterator must be a `Point`.
|
||||
* \tparam WeightIterator is an input iterator over the collection of
|
||||
* weights. The value type of the iterator must be an `FT`.
|
||||
*
|
||||
* \param points_begin is an iterator to the first point.
|
||||
* \param points_end is a past-the-end oterator for the points.
|
||||
* \param weights_begin is an iterator to the weight of the first point.
|
||||
*
|
||||
* \pre The number of weights must be at least equal to the number of
|
||||
* points.
|
||||
*/
|
||||
template < typename PointIterator, typename WeightIterator >
|
||||
WeightedApproximation_3( PointIterator points_begin, PointIterator points_end, WeightIterator weights_begin );
|
||||
|
||||
public:
|
||||
/// \name Point Set.
|
||||
/// \{
|
||||
/// changes a weighted point in the set.
|
||||
/** This invalidates the approximation. `compute()` should be called
|
||||
* after all points have been set.
|
||||
* \pre i must be smaller than the total size of the point set.
|
||||
*/
|
||||
void set_point( unsigned int i, const Point& p, const FT& w );
|
||||
|
||||
/// gives the size of the weighted point set.
|
||||
std::size_t size() const;
|
||||
|
||||
/// \}
|
||||
|
||||
// changes the weighted point set.
|
||||
/* After these points are set, the approximation is immediately computed.
|
||||
*
|
||||
* \tparam PointIterator is an input iterator over the point collection.
|
||||
* The value type of the iterator must be a `Point`.
|
||||
* \tparam WeightIterator is an input iterator over the collection of
|
||||
* weights. The value type of the iterator must be an `FT`.
|
||||
*
|
||||
* \param points_begin is an iterator to the first point.
|
||||
* \param points_end is a past-the-end iterator for the points.
|
||||
* \param weights_begin is an iterator to the weight of the first point.
|
||||
*
|
||||
* \return whether the approximation converges. If the approximation does
|
||||
* not converge this may indicate that the point set is too small, or the
|
||||
* affine hull of the points cannot contain the approximation.
|
||||
*
|
||||
* \pre The points must fit in the approximation.
|
||||
* \pre The number of weights must be at least equal to the number of
|
||||
* points.
|
||||
*/
|
||||
template < typename PointIterator, typename WeightIterator >
|
||||
bool set_points( PointIterator points_begin, PointIterator points_end,
|
||||
WeightIterator weights_begin );
|
||||
|
||||
public:
|
||||
/// \name Approximation
|
||||
/// \{
|
||||
|
||||
/// computes the approximation.
|
||||
/** \return whether the approximation converges. If the approximation does
|
||||
* not converge this may indicate that the point set is too small, or the
|
||||
* affine hull of the points cannot contain the approximation.
|
||||
*/
|
||||
bool compute();
|
||||
|
||||
/// checks whether the approximation has been computed successfully.
|
||||
bool is_computed() const;
|
||||
/// \}
|
||||
|
||||
public:
|
||||
/// \name Fitting
|
||||
/// \{
|
||||
|
||||
/// fits a point to the approximation.
|
||||
/** \param p is the point to fit.
|
||||
*
|
||||
* \return the point on the approximation closest to `p`.
|
||||
*
|
||||
* \pre The approximation must have been computed.
|
||||
*/
|
||||
Point fit( const Point& p );
|
||||
/// \}
|
||||
}; // class WeightedApproximation_3
|
||||
|
|
@ -26,14 +26,9 @@
|
|||
|
||||
\cgalClassifedRefPages
|
||||
|
||||
## Concepts ##
|
||||
|
||||
- `WeightedApproximation_3`
|
||||
|
||||
## Classes ##
|
||||
|
||||
- `CGAL::Scale_space_surface_reconstruction_3<Gt,FS,Sh,wA,Ct>`
|
||||
- `CGAL::Weighted_PCA_approximation_3<Kernel>`
|
||||
|
||||
*/
|
||||
|
||||
|
|
|
|||
|
|
@ -90,7 +90,7 @@ The main class `Scale_space_surface_reconstruction_3` contains all the functiona
|
|||
|
||||
The neighborhood size is estimated using `Orthogonal_k_neighbor_search`. The point set is generally stored in a `Orthogonal_k_neighbor_search::Tree`. When the neighborhood size is estimated, this tree is searched for nearest neighbors.
|
||||
|
||||
The scale-space is constructed at the original scale of the points. An iteration of increasing the scale is computed using a weighted PCA procedure. As described by Digne <i>et al.</i> \cgalCite{cgal:dmsl-ssmrp-11}, unlike similar methods this procedure does not lead to an <em>undesirable clustering effect</em>. By default the efficient \ref thirdpartyEigen library is used for this procedure. It is also possible to provide your own model for the `WeightedApproximation_3` concept. The weighted PCA procedure is performed locally per point, so it can be performed with parallel computing (linking with Intel TBB and passing the `Parallel_tag` to the reconstruction class is required).
|
||||
The scale-space is constructed at the original scale of the points. An iteration of increasing the scale is computed using a weighted PCA procedure. As described by Digne <i>et al.</i> \cgalCite{cgal:dmsl-ssmrp-11}, unlike similar methods this procedure does not lead to an <em>undesirable clustering effect</em>. By default the efficient \ref thirdpartyEigen library is used for this procedure if available. Otherwise, the internal fallback `Internal_diagonalize_traits` is used. It is also possible to provide your own model for the `DiagonalizeTraits` concept. The weighted PCA procedure is performed locally per point, so it can be performed with parallel computing (linking with Intel TBB and passing the `Parallel_tag` to the reconstruction class is required).
|
||||
|
||||
The mesh reconstruction is performed by filtering a \ref Chapter_3D_Alpha_Shapes "3D alpha shape" of the point set at a fixed scale. This filtering constructs a triangle for each regular facet; each singular facet results in two triangles facing opposite directions.
|
||||
|
||||
|
|
|
|||
|
|
@ -4,3 +4,4 @@ STL_Extension
|
|||
Triangulation_3
|
||||
Alpha_shapes_3
|
||||
Spatial_searching
|
||||
Solver_interface
|
||||
|
|
|
|||
|
|
@ -162,21 +162,58 @@ public:
|
|||
return;
|
||||
|
||||
Static_search search(_tree, _pts[i], _nn[i]);
|
||||
Approximation pca( _nn[i] );
|
||||
|
||||
Point barycenter (0., 0., 0.);
|
||||
FT weight_sum = 0.;
|
||||
unsigned int column = 0;
|
||||
// Compute total weight
|
||||
for( typename Static_search::iterator nit = search.begin();
|
||||
nit != search.end() && column < _nn[i];
|
||||
++nit, ++column ) {
|
||||
pca.set_point( column, boost::get<0>(nit->first), 1.0 / _nn[boost::get<1>(nit->first)] );
|
||||
}
|
||||
|
||||
++nit, ++column )
|
||||
weight_sum += (1.0 / _nn[boost::get<1>(nit->first)]);
|
||||
|
||||
column = 0;
|
||||
// Compute barycenter
|
||||
for( typename Static_search::iterator nit = search.begin();
|
||||
nit != search.end() && column < _nn[i];
|
||||
++nit, ++column )
|
||||
{
|
||||
Vector v (CGAL::ORIGIN, boost::get<0>(nit->first));
|
||||
barycenter = barycenter + ((1.0 / _nn[boost::get<1>(nit->first)]) / weight_sum) * v;
|
||||
}
|
||||
|
||||
CGAL::cpp11::array<FT, 6> covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
column = 0;
|
||||
// Compute covariance matrix of Weighted PCA
|
||||
for( typename Static_search::iterator nit = search.begin();
|
||||
nit != search.end() && column < _nn[i];
|
||||
++nit, ++column )
|
||||
{
|
||||
Vector v (barycenter, boost::get<0>(nit->first));
|
||||
FT w = (1.0 / _nn[boost::get<1>(nit->first)]);
|
||||
v = w*v;
|
||||
covariance[0] += w * v.x () * v.x ();
|
||||
covariance[1] += w * v.x () * v.y ();
|
||||
covariance[2] += w * v.x () * v.z ();
|
||||
covariance[3] += w * v.y () * v.y ();
|
||||
covariance[4] += w * v.y () * v.z ();
|
||||
covariance[5] += w * v.z () * v.z ();
|
||||
}
|
||||
|
||||
// Compute the weighted least-squares planar approximation of the point set.
|
||||
if( !pca.compute() )
|
||||
return;
|
||||
CGAL::cpp11::array<FT, 9> eigenvectors = {{ 0., 0., 0.,
|
||||
0., 0., 0.,
|
||||
0., 0., 0. }};
|
||||
CGAL::cpp11::array<FT, 3> eigenvalues = {{ 0., 0., 0. }};
|
||||
wA::diagonalize_selfadjoint_covariance_matrix
|
||||
(covariance, eigenvalues, eigenvectors);
|
||||
|
||||
// The vertex is moved by projecting it onto the plane
|
||||
// through the barycenter and orthogonal to the Eigen vector with smallest Eigen value.
|
||||
_pts[i] = pca.fit( _pts[i] );
|
||||
Vector norm (eigenvectors[0], eigenvectors[1], eigenvectors[2]);
|
||||
Vector b2p (barycenter, _pts[i]);
|
||||
|
||||
_pts[i] = barycenter + b2p - ((norm * b2p) * norm);
|
||||
}
|
||||
}; // class AdvanceSS
|
||||
|
||||
|
|
|
|||
|
|
@ -1,177 +0,0 @@
|
|||
//Copyright (C) 2014 INRIA - Sophia Antipolis
|
||||
//
|
||||
//This program is free software: you can redistribute it and/or modify
|
||||
//it under the terms of the GNU General Public License as published by
|
||||
//the Free Software Foundation, either version 3 of the License, or
|
||||
//(at your option) any later version.
|
||||
//
|
||||
//This program is distributed in the hope that it will be useful,
|
||||
//but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
//MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
//GNU General Public License for more details.
|
||||
//
|
||||
//You should have received a copy of the GNU General Public License
|
||||
//along with this program. If not, see <http://www.gnu.org/licenses/>.
|
||||
//
|
||||
// Author(s): Thijs van Lankveld
|
||||
|
||||
|
||||
#ifndef CGAL_SCALE_SPACE_RECONSTRUCTION_3_WEIGHTED_PCA_PROJECTION_3_H
|
||||
#define CGAL_SCALE_SPACE_RECONSTRUCTION_3_WEIGHTED_PCA_PROJECTION_3_H
|
||||
|
||||
#include <Eigen/Dense>
|
||||
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
/// approximates a point set using a weighted least-squares plane.
|
||||
/** \ingroup PkgScaleSpaceReconstruction3Classes
|
||||
* The weighted least-squares planar approximation contains the barycenter
|
||||
* of the points and is orthogonal to the eigenvector corresponding to the
|
||||
* smallest eigenvalue.
|
||||
*
|
||||
* Point are fitted to this approximation by projecting them orthogonally onto
|
||||
* the weighted least-squares plane.
|
||||
*
|
||||
* This class requires the eigenvector solvers of \ref thirdpartyEigen version
|
||||
* 3.1.2 (or greater).
|
||||
*
|
||||
* \tparam Kernel the geometric traits class of the input and output. It
|
||||
* must have a `RealEmbeddable` field number type.
|
||||
*
|
||||
* \note Irrespective of the geometric traits class, the approximation is
|
||||
* always estimated up to double precision.
|
||||
*
|
||||
* \cgalModels `WeightedApproximation_3`
|
||||
*/
|
||||
template < class Kernel >
|
||||
class Weighted_PCA_approximation_3 {
|
||||
public:
|
||||
typedef typename Kernel::FT FT;
|
||||
typedef typename Kernel::Point_3 Point;
|
||||
|
||||
private:
|
||||
typedef Eigen::Matrix<double, 3, Eigen::Dynamic> Matrix3D; // 3-by-dynamic double-value matrix.
|
||||
typedef Eigen::Array<double, 1, Eigen::Dynamic> Array1D; // 1-by-dynamic double-value array.
|
||||
typedef Eigen::Matrix3d Matrix3; // 3-by-3 double-value matrix.
|
||||
typedef Eigen::Vector3d Vector3; // 3-by-1 double-value matrix.
|
||||
typedef Eigen::SelfAdjointEigenSolver< Matrix3 > EigenSolver; // Eigen value decomposition solver.
|
||||
|
||||
private:
|
||||
bool _comp; // Whether the eigenvalues are computed.
|
||||
|
||||
Matrix3D _pts; // points.
|
||||
Array1D _wts; // weights.
|
||||
|
||||
Vector3 _bary; // barycenter.
|
||||
Vector3 _norm; // normal.
|
||||
|
||||
public:
|
||||
// constructs an default approximation to hold the points.
|
||||
/* \param size is the number of points that will be added.
|
||||
*/
|
||||
Weighted_PCA_approximation_3( unsigned int size ): _comp(false), _pts(3,size), _wts(1,size) {}
|
||||
|
||||
// computes the weighted least-squares planar approximation of a point set.
|
||||
/* Similar to constructing an empty projection and calling
|
||||
* <code>[set_points(points_begin, points_end, weights_begin)](\ref WeightedApproximation_3::set_points )</code>
|
||||
*
|
||||
* \tparam PointIterator is an input iterator over the point collection.
|
||||
* The value type of the iterator must be a `Point`.
|
||||
* \tparam WeightIterator is an input iterator over the collection of
|
||||
* weights. The value type of the iterator must be an `FT`.
|
||||
*
|
||||
* \param points_begin is an iterator to the first point.
|
||||
* \param points_end is a past-the-end oterator for the points.
|
||||
* \param weights_begin is an iterator to the weight of the first point.
|
||||
*/
|
||||
template < typename PointIterator, typename WeightIterator >
|
||||
Weighted_PCA_approximation_3( PointIterator points_begin, PointIterator points_end, WeightIterator weights_begin )
|
||||
: _comp(false) {
|
||||
std::size_t size = std::distance( points_begin, points_end );
|
||||
_pts = Matrix3D(3,size);
|
||||
_wts = Array1D(1,size);
|
||||
set_points( points_begin, points_end, weights_begin );
|
||||
}
|
||||
|
||||
public:
|
||||
// sets a weighted point in the collection.
|
||||
void set_point( unsigned int i, const Point& p, const FT& w ) {
|
||||
_pts( 0, i ) = CGAL::to_double( p[0] );
|
||||
_pts( 1, i ) = CGAL::to_double( p[1] );
|
||||
_pts( 2, i ) = CGAL::to_double( p[2] );
|
||||
_wts( i ) = CGAL::to_double( w );
|
||||
_comp = false;
|
||||
}
|
||||
|
||||
// sets the weighted points and compute PCA.
|
||||
template < typename PointIterator, typename WeightIterator >
|
||||
bool set_points( PointIterator points_begin, PointIterator points_end, WeightIterator weights_begin ) {
|
||||
for( unsigned int column = 0; points_begin != points_end; ++column, ++points_begin, ++weights_begin ) {
|
||||
_pts( 0, column ) = CGAL::to_double( (*points_begin)[0] );
|
||||
_pts( 1, column ) = CGAL::to_double( (*points_begin)[1] );
|
||||
_pts( 2, column ) = CGAL::to_double( (*points_begin)[2] );
|
||||
_wts( column ) = CGAL::to_double( *weights_begin );
|
||||
}
|
||||
return compute();
|
||||
}
|
||||
|
||||
// gives the size of the weighted point set.
|
||||
std::size_t size() const { return _pts.cols(); }
|
||||
|
||||
// compute weighted PCA.
|
||||
bool compute() {
|
||||
// Construct the barycenter.
|
||||
_bary = ( _pts.array().rowwise() * _wts ).rowwise().sum() / _wts.sum();
|
||||
|
||||
// Replace the points by their difference with the barycenter.
|
||||
_pts = ( _pts.colwise() - _bary ).array().rowwise() * _wts;
|
||||
|
||||
// Construct the weighted covariance matrix.
|
||||
Matrix3 covar = Matrix3::Zero();
|
||||
for( int column = 0; column < _pts.cols(); ++column )
|
||||
covar += _wts.matrix()(column) * _pts.col(column) * _pts.col(column).transpose();
|
||||
|
||||
// Construct the Eigen system.
|
||||
EigenSolver solver( covar );
|
||||
|
||||
// If the Eigen system does not converge, the vertex is not moved.
|
||||
if( solver.info() != Eigen::Success )
|
||||
return false;
|
||||
|
||||
// Find the Eigen vector with the smallest Eigen value.
|
||||
std::ptrdiff_t index;
|
||||
solver.eigenvalues().minCoeff( &index );
|
||||
if( solver.eigenvectors().col( index ).imag() != Vector3::Zero() ) {
|
||||
// This should actually never happen,
|
||||
// because the covariance matrix is symmetric!
|
||||
CGAL_assertion( false );
|
||||
return false;
|
||||
}
|
||||
|
||||
// The normal is the Eigen vector with smallest Eigen value.
|
||||
_norm = solver.eigenvectors().col( index ).real();
|
||||
_comp = true;
|
||||
return true;
|
||||
}
|
||||
|
||||
// checks whether the weighted least-squares approximating plane has been computed.
|
||||
bool is_computed() const { return _comp; }
|
||||
|
||||
public:
|
||||
// projects a point onto the weighted PCA plane.
|
||||
Point fit( const Point& p ) {
|
||||
CGAL_assertion( _comp );
|
||||
// The point is moved by projecting it onto the plane through the
|
||||
// barycenter and orthogonal to the normal.
|
||||
Vector3 to_p = Vector3( to_double( p[0] ),
|
||||
to_double( p[1] ),
|
||||
to_double( p[2] ) ) - _bary;
|
||||
Vector3 proj = _bary + to_p - ( _norm.dot(to_p) * _norm );
|
||||
return Point( proj(0), proj(1), proj(2) );
|
||||
}
|
||||
}; // class Weighted_PCA_approximation_3
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
#endif // CGAL_SCALE_SPACE_RECONSTRUCTION_3_WEIGHTED_PCA_PROJECTION_3_H
|
||||
|
|
@ -36,13 +36,10 @@
|
|||
#include <CGAL/Orthogonal_k_neighbor_search.h>
|
||||
#include <CGAL/Fuzzy_sphere.h>
|
||||
#include <CGAL/Random.h>
|
||||
#include <CGAL/Default_diagonalize_traits.h>
|
||||
|
||||
#include <CGAL/Scale_space_reconstruction_3/Shape_construction_3.h>
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
#include <CGAL/Scale_space_reconstruction_3/Weighted_PCA_approximation_3.h>
|
||||
#endif // CGAL_EIGEN3_ENABLED
|
||||
|
||||
#include <boost/mpl/and.hpp>
|
||||
|
||||
namespace CGAL {
|
||||
|
|
@ -99,25 +96,22 @@ namespace CGAL {
|
|||
* only has an impact on the run-time.
|
||||
* \tparam Sh determines whether to collect the surface per shell. It
|
||||
* must be a `Boolean_tag` type. The default value is `Tag_true`.
|
||||
* \tparam wA must be a model of `WeightedPCAProjection_3` and determines how
|
||||
* to approximate a weighted point set. If \ref thirdpartyEigen 3.1.2 (or
|
||||
* greater) is available and CGAL_EIGEN3_ENABLED is defined, then
|
||||
* `Weighted_PCA_approximation_3<DelaunayTriangulationTraits_3>` is used by default.
|
||||
* \tparam wA must be a model of `DiagonalizeTraits` and determines
|
||||
* how to diagonalize a weighted covariance matrix to approximate a
|
||||
* weighted point set. It can be omitted: if Eigen 3 (or greater) is
|
||||
* available and `CGAL_EIGEN3_ENABLED` is defined then an overload
|
||||
* using `Eigen_diagonalize_traits` is provided. Otherwise, the
|
||||
* internal implementation `Internal_diagonalize_traits` is used.
|
||||
* \tparam Ct indicates whether to use concurrent processing. It must be
|
||||
* either `Sequential_tag` or `Parallel_tag` (the default value).
|
||||
*/
|
||||
template < class Gt, class FS = Tag_true, class Sh = Tag_true, class wA = Default, class Ct = Parallel_tag >
|
||||
template < class Gt, class FS = Tag_true, class Sh = Tag_true,
|
||||
class wA = Default_diagonalize_traits<typename Gt::FT, 3>, class Ct = Parallel_tag >
|
||||
class Scale_space_surface_reconstruction_3 {
|
||||
typedef typename Default::Get< wA,
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
Weighted_PCA_approximation_3<Gt>
|
||||
#else // CGAL_EIGEN3_ENABLED
|
||||
void
|
||||
#endif // CGAL_EIGEN3_ENABLED
|
||||
>::type Approximation;
|
||||
|
||||
public:
|
||||
typedef typename Gt::Point_3 Point; ///< defines the point type.
|
||||
typedef typename Gt::Vector_3 Vector; ///< defines the vector type.
|
||||
typedef boost::tuple<Point,int> Point_and_int;
|
||||
|
||||
private:
|
||||
|
|
|
|||
|
|
@ -0,0 +1,53 @@
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_diagonalize_traits` provides an interface to the
|
||||
diagonalization of covariance matrices of \ref thirdpartyEigen
|
||||
"Eigen".
|
||||
|
||||
The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be
|
||||
available on the system.
|
||||
|
||||
\cgalModels `DiagonalizeTraits`
|
||||
|
||||
|
||||
\tparam FT Number type
|
||||
\tparam dim Dimension of the matrices and vectors
|
||||
|
||||
\sa http://eigen.tuxfamily.org
|
||||
|
||||
Example
|
||||
--------------
|
||||
|
||||
|
||||
*/
|
||||
|
||||
|
||||
|
||||
template <typename FT, unsigned int dim = 3>
|
||||
class Eigen_diagonalize_traits{
|
||||
|
||||
public:
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues);
|
||||
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues,
|
||||
cpp11::array<FT, dim * dim>& eigenvectors);
|
||||
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT,dim> &normal);
|
||||
|
||||
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
|
|
@ -2,24 +2,18 @@
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationAlgebra
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_sparse_matrix` is a C++ wrapper around \ref thirdpartyEigen "Eigen" matrix type `Eigen::SparseMatrix`
|
||||
The class `Eigen_sparse_matrix` is a wrapper around \ref thirdpartyEigen "Eigen" matrix type <a href="http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html">`Eigen::SparseMatrix` </a>
|
||||
that represents general matrices, be they symmetric or not.
|
||||
The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be available on the system.
|
||||
|
||||
\cgalModels `SparseLinearAlgebraTraits_d::Matrix`
|
||||
|
||||
Parameters
|
||||
--------------
|
||||
|
||||
`T`: Number type.
|
||||
\tparam T Number type.
|
||||
|
||||
\sa `CGAL::Eigen_solver_traits<T>`
|
||||
\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
|
||||
\sa `CGAL::Eigen_vector<T>`
|
||||
\sa http://eigen.tuxfamily.org
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
class Eigen_sparse_matrix {
|
||||
|
|
@ -41,23 +35,19 @@ typedef unspecified_type EigenType;
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationAlgebra
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_sparse_symmetric_matrix` is a C++ wrapper around \ref thirdpartyEigen "Eigen" matrix type `Eigen::SparseMatrix`.
|
||||
The class `Eigen_sparse_symmetric_matrix` is a wrapper around \ref thirdpartyEigen "Eigen" matrix type <a href="http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html">`Eigen::SparseMatrix` </a>
|
||||
|
||||
As the matrix is symmetric only the lower triangle part is stored.
|
||||
|
||||
\cgalModels `SparseLinearAlgebraTraits_d::Matrix`
|
||||
|
||||
Parameters
|
||||
--------------
|
||||
|
||||
`T`: Number type.
|
||||
\tparam T Number type.
|
||||
|
||||
\sa `CGAL::Eigen_solver_traits<T>`
|
||||
\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
|
||||
\sa `CGAL::Eigen_sparse_matrix<T>`
|
||||
\sa `CGAL::Eigen_vector<T>`
|
||||
\sa http://eigen.tuxfamily.org
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
|
|
@ -75,4 +65,29 @@ typedef unspecified_type EigenType;
|
|||
/// @}
|
||||
|
||||
}; /* end Eigen_sparse_symmetric_matrix */
|
||||
|
||||
|
||||
/*!
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_matrix` is a wrapper around \ref thirdpartyEigen "Eigen"
|
||||
matrix type
|
||||
<a href="http://eigen.tuxfamily.org/dox/classEigen_1_1Matrix.html">`Eigen::Matrix`</a>.
|
||||
|
||||
|
||||
\cgalModels `SvdTraits::Matrix`
|
||||
|
||||
\tparam T Number type.
|
||||
|
||||
\sa `CGAL::Eigen_svd`
|
||||
\sa `CGAL::Eigen_vector<T>`
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
class Eigen_matrix {
|
||||
public:
|
||||
|
||||
};
|
||||
|
||||
|
||||
} /* end namespace CGAL */
|
||||
|
|
@ -2,18 +2,15 @@
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationAlgebra
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_solver_traits` provides an interface to the sparse solvers of \ref thirdpartyEigen "Eigen".
|
||||
The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be available on the system.
|
||||
|
||||
\cgalModels `#SparseLinearAlgebraTraitsWithFactor_d` and `#NormalEquationSparseLinearAlgebraTraits_d`
|
||||
\cgalModels `SparseLinearAlgebraTraitsWithFactor_d` and `NormalEquationSparseLinearAlgebraTraits_d`
|
||||
|
||||
Parameters
|
||||
--------------
|
||||
|
||||
`T`: a sparse solver of \ref thirdpartyEigen "Eigen". The default solver is the iterative bi-congugate gradient stabilized solver
|
||||
`Eigen::BiCGSTAB` for `double`.
|
||||
\tparam T A sparse solver of \ref thirdpartyEigen "Eigen". The default solver is the iterative bi-congugate gradient stabilized solver `Eigen::BiCGSTAB` for `double`.
|
||||
|
||||
\sa `CGAL::Eigen_sparse_matrix<T>`
|
||||
\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
|
||||
|
|
@ -2,11 +2,11 @@
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgJet_fitting_3
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_svd` provides an algorithm to solve in the least
|
||||
square sense a linear system with a singular value decomposition using
|
||||
\ref thirdpartyEigen. The field type is `double`.
|
||||
\ref thirdpartyEigen.
|
||||
|
||||
\cgalModels `SvdTraits`
|
||||
|
||||
|
|
@ -15,7 +15,11 @@ square sense a linear system with a singular value decomposition using
|
|||
class Eigen_svd {
|
||||
public:
|
||||
|
||||
/// @}
|
||||
typedef double FT;
|
||||
|
||||
typedef Eigen_vector<FT> Vector;
|
||||
|
||||
typedef Eigen_matrix<FT> Matrix;
|
||||
|
||||
}; /* end Eigen_svd */
|
||||
} /* end namespace CGAL */
|
||||
|
|
@ -2,22 +2,21 @@
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationAlgebra
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Eigen_vector` is a C++ wrapper around \ref thirdpartyEigen "Eigen" vector, which is a simple array of numbers.
|
||||
The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be available on the system.
|
||||
The class `Eigen_vector` is a wrapper around \ref thirdpartyEigen "Eigen" vector
|
||||
type <a href="http://eigen.tuxfamily.org/dox/classEigen_1_1Matrix.html"> </a>,
|
||||
which is a simple array of numbers.
|
||||
|
||||
\cgalModels `SvdTraits::Vector`
|
||||
\cgalModels `SparseLinearAlgebraTraits_d::Vector`.
|
||||
|
||||
Parameters
|
||||
--------------
|
||||
|
||||
`T`: Number type.
|
||||
\tparam T Number type.
|
||||
|
||||
\sa `CGAL::Eigen_solver_traits<T>`
|
||||
\sa `CGAL::Eigen_sparse_matrix<T>`
|
||||
\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
|
||||
\sa http://eigen.tuxfamily.org
|
||||
|
||||
*/
|
||||
template< typename T >
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
namespace CGAL {
|
||||
|
||||
/*!
|
||||
\ingroup PkgSolver
|
||||
|
||||
The class `Internal_diagonalize_traits` provides an internal
|
||||
implementation for the diagonalization of Variance-Covariance
|
||||
Matrices.
|
||||
|
||||
\cgalModels `DiagonalizeTraits`
|
||||
|
||||
\tparam FT Number type
|
||||
\tparam dim Dimension of the matrices and vectors
|
||||
|
||||
Example
|
||||
--------------
|
||||
|
||||
*/
|
||||
|
||||
|
||||
|
||||
template <typename FT, unsigned int dim = 3>
|
||||
class Internal_diagonalize_traits{
|
||||
|
||||
public:
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues);
|
||||
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues,
|
||||
cpp11::array<FT, dim * dim>& eigenvectors);
|
||||
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT,dim> &normal);
|
||||
|
||||
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
/*!
|
||||
\ingroup PkgSolverConcepts
|
||||
\cgalConcept
|
||||
|
||||
Concept providing functions to extract eigenvectors and eigenvalue
|
||||
from covariance matrices represented by an array `a`, using symmetric
|
||||
diagonalization. For example, a matrix of dimension 3 is defined as
|
||||
follows:
|
||||
<center>
|
||||
\f$ \begin{bmatrix}
|
||||
a[0] & a[1] & a[2] \\
|
||||
a[1] & a[3] & a[4] \\
|
||||
a[2] & a[4] & a[5] \\
|
||||
\end{bmatrix}\f$
|
||||
</center>
|
||||
\cgalHasModel `CGAL::Eigen_diagonalize_traits`
|
||||
\cgalHasModel `CGAL::Internal_diagonalize_traits`
|
||||
*/
|
||||
template <typename FT, unsigned int dim = 3>
|
||||
class DiagonalizeTraits
|
||||
{
|
||||
public:
|
||||
/// fill `eigenvalues` with the eigenvalues of the covariance matrix represented by `cov`.
|
||||
/// Eigenvalues are sorted by increasing order.
|
||||
/// \return `true` if the operation was successful and `false` otherwise.
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues);
|
||||
|
||||
/// fill `eigenvalues` with the eigenvalues and `eigenvectors` with
|
||||
/// the eigenvectors of the covariance matrix represented by `cov`.
|
||||
/// Eigenvalues are sorted by increasing order.
|
||||
/// \return `true` if the operation was successful and `false`
|
||||
/// otherwise.
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues,
|
||||
cpp11::array<FT, dim * dim>& eigenvectors);
|
||||
|
||||
|
||||
/// Extract the eigenvector associated to the largest eigenvalue
|
||||
/// of the covariance matrix represented by `cov`.
|
||||
/// \return `true` if the operation was successful and `false` otherwise.
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT,dim> &normal);
|
||||
};
|
||||
|
||||
|
|
@ -1,6 +1,7 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgMeanCurvatureSkeleton3Concepts
|
||||
\ingroup PkgSolverConcepts
|
||||
|
||||
\cgalConcept
|
||||
|
||||
|
||||
|
|
@ -1,6 +1,6 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgSurfaceModelingConcepts
|
||||
\ingroup PkgSolverConcepts
|
||||
\cgalConcept
|
||||
|
||||
@brief Concept describing the set of requirements for a direct sparse linear system solver with factorization.
|
||||
|
|
@ -31,16 +31,16 @@ SparseLinearAlgebraTraitsWithFactor_d();
|
|||
/// @{
|
||||
|
||||
/*!
|
||||
Factorize the sparse matrix A.
|
||||
This factorization is used in SparseLinearAlgebraTraitsWithFactor_d::linear_solver to solve the system for different right-hand side vectors.
|
||||
Factorize the sparse matrix `A`.
|
||||
This factorization is used in `SparseLinearAlgebraTraitsWithFactor_d::linear_solver()` to solve the system for different right-hand side vectors.
|
||||
See `::SparseLinearAlgebraTraits_d::linear_solver()` for the description of `D`.
|
||||
@return true if the factorization is successful
|
||||
@return `true` if the factorization is successful
|
||||
*/
|
||||
bool factor(const Matrix& A, NT& D);
|
||||
|
||||
/*!
|
||||
Solve the sparse linear system \f$ A \times X = B\f$, with \f$ A \f$ being the matrix provided in SparseLinearAlgebraTraitsWithFactor_d::factor.
|
||||
@return true if the solver is successful
|
||||
Solve the sparse linear system \f$ A \times X = B\f$, with \f$ A \f$ being the matrix provided in `SparseLinearAlgebraTraitsWithFactor_d::factor()`.
|
||||
@return `true` if the solver is successful
|
||||
*/
|
||||
bool linear_solver(const Vector& B, Vector& X);
|
||||
|
||||
|
|
@ -1,18 +1,14 @@
|
|||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationConcepts
|
||||
\ingroup PkgSolverConcepts
|
||||
|
||||
\cgalConcept
|
||||
|
||||
The concept `SparseLinearAlgebraTraits_d` is used to solve sparse linear systems <I>A\f$ \times \f$ X = B</I>.
|
||||
|
||||
\cgalRefines `LinearAlgebraTraits_d`
|
||||
|
||||
\cgalHasModel `CGAL::Eigen_solver_traits<T>`
|
||||
\cgalHasModel `OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
|
||||
\cgalHasModel `OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
|
||||
|
||||
\sa `SparseLinearAlgebraTraits_d::Matrix`
|
||||
\sa `SparseLinearAlgebraTraits_d::Vector`
|
||||
|
||||
*/
|
||||
|
||||
|
|
@ -66,23 +62,23 @@ bool linear_solver(const Matrix& A, const Vector& B, Vector& X, NT& D);
|
|||
|
||||
/// @}
|
||||
|
||||
}; /* end SparseLinearAlgebraTraits_d */
|
||||
|
||||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationConcepts
|
||||
\cgalConcept
|
||||
|
||||
`SparseLinearAlgebraTraits_d::Vector` is a concept of a vector that can be multiplied by a sparse matrix.
|
||||
|
||||
\cgalRefines `LinearAlgebraTraits_d::Vector`
|
||||
|
||||
\cgalHasModel `CGAL::Eigen_vector<T>`
|
||||
\cgalHasModel `OpenNL::FullVector<T>` in `OpenNL` package
|
||||
|
||||
\sa `SparseLinearAlgebraTraits_d`
|
||||
\sa `SparseLinearAlgebraTraits_d::Matrix`
|
||||
|
||||
*/
|
||||
|
||||
class Vector {
|
||||
|
||||
class SparseLinearAlgebraTraits_d::Vector {
|
||||
public:
|
||||
|
||||
/// \name Types
|
||||
|
|
@ -142,23 +138,20 @@ NT& operator[](int row);
|
|||
}; /* end Vector */
|
||||
|
||||
/*!
|
||||
\ingroup PkgSurfaceParameterizationConcepts
|
||||
|
||||
\cgalConcept
|
||||
|
||||
`SparseLinearAlgebraTraits_d::Matrix` is a concept of a sparse matrix class.
|
||||
|
||||
\cgalRefines `LinearAlgebraTraits_d::Matrix`
|
||||
|
||||
\cgalHasModel `CGAL::Eigen_sparse_matrix<T>`
|
||||
\cgalHasModel `CGAL::Eigen_sparse_symmetric_matrix<T>`
|
||||
\cgalHasModel `OpenNL::SparseMatrix<T>` in `OpenNL` package
|
||||
|
||||
\sa `SparseLinearAlgebraTraits_d`
|
||||
\sa `SparseLinearAlgebraTraits_d::Vector`
|
||||
|
||||
*/
|
||||
|
||||
class Matrix {
|
||||
class SparseLinearAlgebraTraits_d::Matrix {
|
||||
public:
|
||||
|
||||
/// \name Types
|
||||
|
|
@ -243,6 +236,3 @@ void set_coef(int row, int column, NT value, bool new_coef = false);
|
|||
|
||||
}; /* end Matrix */
|
||||
|
||||
|
||||
}; /* end SparseLinearAlgebraTraits_d */
|
||||
|
||||
|
|
@ -1,23 +1,12 @@
|
|||
/*!
|
||||
\ingroup PkgJet_fitting_3Concepts
|
||||
\ingroup PkgSolverConcepts
|
||||
\cgalConcept
|
||||
|
||||
The concept `SvdTraits` describes the set of requirements to be
|
||||
fulfilled by any class used to instantiate the third template
|
||||
parameter of the class
|
||||
`CGAL::Monge_via_jet_fitting<DataKernel,LocalKernel,SvdTraits>`.
|
||||
|
||||
It describes the linear algebra types and algorithms needed by the
|
||||
class `CGAL::Monge_via_jet_fitting`.
|
||||
|
||||
\cgalHeading{Requirements}
|
||||
|
||||
The scalar type, `SvdTraits::FT`, must be the same as that of
|
||||
the `LocalKernel` concept : `LocalKernel::FT`.
|
||||
The concept `SvdTraits` describes the linear algebra types and algorithms needed
|
||||
to solve in the least square sense a linear system with a singular value decomposition
|
||||
|
||||
\cgalHasModel `CGAL::Eigen_svd`
|
||||
|
||||
\sa `LocalKernel`
|
||||
\cgalHasModel `CGAL::Lapack_svd`
|
||||
|
||||
*/
|
||||
class SvdTraits {
|
||||
|
|
@ -39,7 +28,7 @@ public:
|
|||
/*!
|
||||
The matrix type, model of the concept `SvdTraits::Matrix`.
|
||||
*/
|
||||
typedef unspecified_type matrix;
|
||||
typedef unspecified_type Matrix;
|
||||
|
||||
/// @}
|
||||
|
||||
|
|
@ -60,9 +49,10 @@ public:
|
|||
}; /* end SvdTraits */
|
||||
|
||||
/*!
|
||||
\ingroup PkgJet_fitting_3Concepts
|
||||
\cgalConcept
|
||||
Concept of vector type used by the concept SvdTraits.
|
||||
Concept of vector type used by the concept `SvdTraits`.
|
||||
|
||||
\cgalHasModel `CGAL::Eigen_vector<T>`
|
||||
*/
|
||||
class SvdTraits::Vector {
|
||||
public:
|
||||
|
|
@ -76,12 +66,12 @@ public:
|
|||
size_t size();
|
||||
|
||||
/*!
|
||||
return the \f$ i^{th}\f$ entry, \f$ i\f$ from \f$ 0\f$ to \f$ size()-1\f$.
|
||||
return the `i`th entry, `i` from `0` to `size()-1`.
|
||||
*/
|
||||
FT operator()(size_t i);
|
||||
|
||||
/*!
|
||||
set the \f$ i^{th}\f$ entry to `value`.
|
||||
set the `i`'th entry to `value`.
|
||||
*/
|
||||
void set(size_t i, const FT value);
|
||||
|
||||
|
|
@ -93,9 +83,10 @@ public:
|
|||
|
||||
|
||||
/*!
|
||||
\ingroup PkgJet_fitting_3Concepts
|
||||
\cgalConcept
|
||||
Concept of matrix type used by the concept SvdTraits.
|
||||
Concept of matrix type used by the concept `SvdTraits`.
|
||||
|
||||
\cgalHasModel `CGAL::Eigen_matrix<T>`
|
||||
*/
|
||||
class SvdTraits::Matrix {
|
||||
public:
|
||||
|
|
@ -115,13 +106,13 @@ public:
|
|||
size_t number_of_columns();
|
||||
|
||||
/*!
|
||||
return the entry at row \f$ i\f$ and column \f$ j\f$, \f$ i\f$ from \f$ 0\f$ to `number_of_rows - 1`,
|
||||
\f$ j\f$ from \f$ 0\f$ to `number_of_columns - 1`.
|
||||
return the entry at row `i` and column `j`, `i` from `0` to `number_of_rows - 1`,
|
||||
`j` from `0` to `number_of_columns - 1`.
|
||||
*/
|
||||
FT operator()(size_t i, size_t j);
|
||||
|
||||
/*!
|
||||
set the entry at row \f$ i\f$ and column \f$ j\f$ to \f$ value\f$.
|
||||
set the entry at row `i` and column `j` to `value`.
|
||||
*/
|
||||
void set(size_t i, size_t j, const FT value);
|
||||
};
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
@INCLUDE = ${CGAL_DOC_PACKAGE_DEFAULTS}
|
||||
|
||||
PROJECT_NAME = "CGAL ${CGAL_CREATED_VERSION_NUM} - CGAL and Solvers"
|
||||
INPUT = ${CMAKE_SOURCE_DIR}/Solver_interface/doc/Solver_interface/
|
||||
EXAMPLE_PATH = ${CMAKE_SOURCE_DIR}/Solver_interface/examples/Solver_interface/
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,50 @@
|
|||
/// \defgroup PkgSolver CGAL and Solvers Reference
|
||||
|
||||
/// \defgroup PkgSolverConcepts Concepts
|
||||
/// \ingroup PkgSolver
|
||||
///
|
||||
|
||||
|
||||
/*!
|
||||
\addtogroup PkgSolver
|
||||
\cgalPkgDescriptionBegin{CGAL and Solvers,PkgSolverSummary}
|
||||
\cgalPkgPicture{solver.png}
|
||||
\cgalPkgSummaryBegin
|
||||
\cgalPkgAuthors{CGAL Editorial Board }
|
||||
\cgalPkgDesc{This package provides concepts and models for solving linear systems with dense or sparse matrices.}
|
||||
\cgalPkgManuals{Chapter_CGAL_and_Solvers,PkgSolver}
|
||||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.7}
|
||||
\cgalPkgBib{cgal:eb-solver }
|
||||
\cgalPkgLicense{\ref licensesLGPL "LGPL"}
|
||||
\cgalPkgShortInfoEnd
|
||||
\cgalPkgDescriptionEnd
|
||||
|
||||
\cgalClassifedRefPages
|
||||
|
||||
## Concepts ##
|
||||
|
||||
- `DiagonalizeTraits`
|
||||
- `SparseLinearAlgebraTraits_d`
|
||||
- `SparseLinearAlgebraTraitsWithFactor_d`
|
||||
- `SvdTraits`
|
||||
|
||||
|
||||
## Classes ##
|
||||
|
||||
- `CGAL::Eigen_solver_traits`
|
||||
- `CGAL::Eigen_svd`
|
||||
- `CGAL::Eigen_diagonalize_traits`
|
||||
- `CGAL::Eigen_matrix`
|
||||
- `CGAL::Eigen_vector`
|
||||
- `CGAL::Eigen_sparse_matrix`
|
||||
- `CGAL::Eigen_sparse_symmetric_matrix`
|
||||
- `CGAL::Internal_diagonalize_traits`
|
||||
- `CGAL::Lapack_svd`
|
||||
|
||||
*/
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,107 @@
|
|||
namespace CGAL {
|
||||
/*!
|
||||
|
||||
\mainpage User Manual
|
||||
\anchor Chapter_CGAL_and_Solvers
|
||||
\anchor chapterSolvers
|
||||
\cgalAutoToc
|
||||
\authors %CGAL Editorial Board
|
||||
|
||||
Several \cgal packages have to solve linear systems with dense or
|
||||
sparse matrices. This package provides concepts and models for that
|
||||
purpose.
|
||||
|
||||
We generally provide models using the \ref thirdpartyEigen
|
||||
library. Wrappers for the Eigen classes `Eigen_matrix` and
|
||||
`Eigen_vector` are also provided when needed.
|
||||
|
||||
It is straightforward to develop equivalent models for
|
||||
other solvers, for example those found in the <a
|
||||
href="https://software.intel.com/en-us/intel-mkl">Intel Math Kernel
|
||||
Library (MKL)</a>.
|
||||
|
||||
|
||||
\section SectionSolverDiagonalize Matrix Diagonalization
|
||||
|
||||
The concept `DiagonalizeTraits<T,dim>` defines an interface for the
|
||||
diagonalization and computation of eigenvectors and eigenvalues of a
|
||||
symmetric matrix. `T` is the number type and `dim` is the dimension of
|
||||
the matrices and vector (set to 3 by default). We provide two models
|
||||
for this concept:
|
||||
|
||||
- `Eigen_diagonalize_traits<T,dim>` uses the \ref thirdpartyEigen library.
|
||||
- `Internal_diagonalize_traits<T,dim>` is an internal implementation that does not
|
||||
depend on another library.
|
||||
|
||||
Although both models achieve the same computation,
|
||||
`Eigen_diagonalize_traits<T,dim>` is faster and should thus be used if the
|
||||
\ref thirdpartyEigen library is available. The eigenvalues are stored
|
||||
in ascending order and eigenvectors are stored in accordance.
|
||||
|
||||
This is an example of an eigendecomposition of a matrix using this
|
||||
class:
|
||||
|
||||
|
||||
\cgalExample{Solver_interface/diagonalize_matrix.cpp}
|
||||
|
||||
|
||||
\section SectionSolverSVD Singular Value Decomposition
|
||||
|
||||
The concept `SvdTraits` defines an interface for solving in the least
|
||||
square sense a linear system with a singular value decomposition. The
|
||||
field type is `double`. We provide two models for this concept:
|
||||
|
||||
- `Eigen_svd` uses the \ref thirdpartyEigen library.
|
||||
- `Lapack_svd` uses the \ref thirdpartyLapack library.
|
||||
|
||||
Here is a simple example that shows how to handle matrices, vectors
|
||||
and this solver:
|
||||
|
||||
\cgalExample{Solver_interface/singular_value_decomposition.cpp}
|
||||
|
||||
|
||||
|
||||
|
||||
\section SectionSolverSparse Sparse Solvers
|
||||
|
||||
We define 3 concepts for sparse linear algebra:
|
||||
|
||||
- `SparseLinearAlgebraTraits_d`
|
||||
- `SparseLinearAlgebraTraitsWithFactor_d`
|
||||
- `NormalEquationSparseLinearAlgebraTraits_d`
|
||||
|
||||
An interface to the sparse solvers from the \ref thirdpartyEigen
|
||||
library is provided as a model for these 3 concepts through the class
|
||||
`Eigen_solver_traits<T>`. This solver traits class can be used for an
|
||||
iterative or a direct, symmetric or general sparse solvers. The
|
||||
specific solver to be used must be given as template parameter.
|
||||
|
||||
Each \cgal package using a sparse solver specifies which type of matrix
|
||||
and solver is required:
|
||||
|
||||
\code{.cpp}
|
||||
|
||||
typedef CGAL::Eigen_sparse_matrix<double>::EigenType EigenMatrix;
|
||||
|
||||
//iterative general solver
|
||||
typedef CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<EigenMatrix> > Iterative_general_solver;
|
||||
|
||||
//iterative symmetric solver
|
||||
typedef CGAL::Eigen_solver_traits< Eigen::ConjugateGradient<EigenMatrix> > Iterative_symmetric_solver;
|
||||
|
||||
//direct symmetric solver
|
||||
typedef CGAL::Eigen_solver_traits< Eigen::SimplicialCholesky<EigenMatrix> > Direct_symmetric_solver;
|
||||
|
||||
\endcode
|
||||
|
||||
Here is an example that shows how to fill the sparse matrix and call
|
||||
the solver:
|
||||
|
||||
\cgalExample{Solver_interface/sparse_solvers.cpp}
|
||||
|
||||
|
||||
|
||||
|
||||
*/
|
||||
} /* namespace CGAL */
|
||||
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
Manual
|
||||
Kernel_23
|
||||
STL_Extension
|
||||
Algebraic_foundations
|
||||
Miscellany
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
/*!
|
||||
\example Solver_interface/diagonalize_matrix.cpp
|
||||
\example Solver_interface/singular_value_decomposition.cpp
|
||||
\example Solver_interface/sparse_solvers.cpp
|
||||
*/
|
||||
Binary file not shown.
|
After Width: | Height: | Size: 909 B |
|
|
@ -0,0 +1,45 @@
|
|||
# Created by the script cgal_create_cmake_script
|
||||
# This is the CMake script for compiling a CGAL application.
|
||||
|
||||
|
||||
project( examples_ )
|
||||
|
||||
cmake_minimum_required(VERSION 2.8.10)
|
||||
|
||||
find_package(CGAL QUIET COMPONENTS Core )
|
||||
|
||||
if ( CGAL_FOUND )
|
||||
|
||||
include( ${CGAL_USE_FILE} )
|
||||
|
||||
include( CGAL_CreateSingleSourceCGALProgram )
|
||||
|
||||
include_directories (BEFORE "../include")
|
||||
|
||||
# Use Eigen or BLAS and LAPACK (optional)
|
||||
find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
|
||||
if (NOT EIGEN3_FOUND)
|
||||
find_package(LAPACK)
|
||||
if(LAPACK_FOUND)
|
||||
include( ${LAPACK_USE_FILE} )
|
||||
endif(LAPACK_FOUND)
|
||||
else()
|
||||
include( ${EIGEN3_USE_FILE} )
|
||||
endif()
|
||||
|
||||
if(EIGEN3_FOUND OR LAPACK_FOUND)
|
||||
create_single_source_cgal_program( "singular_value_decomposition.cpp" )
|
||||
endif()
|
||||
|
||||
if(EIGEN3_FOUND)
|
||||
create_single_source_cgal_program( "sparse_solvers.cpp" )
|
||||
endif()
|
||||
|
||||
create_single_source_cgal_program( "diagonalize_matrix.cpp" )
|
||||
|
||||
else()
|
||||
|
||||
message(STATUS "This program requires the CGAL library, and will not be compiled.")
|
||||
|
||||
endif()
|
||||
|
||||
|
|
@ -0,0 +1,51 @@
|
|||
#include <iostream>
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
#include <CGAL/Eigen_diagonalize_traits.h>
|
||||
#else
|
||||
#include <CGAL/Internal_diagonalize_traits.h>
|
||||
#endif
|
||||
|
||||
typedef double FT;
|
||||
typedef CGAL::cpp11::array<FT, 6> Eigen_matrix;
|
||||
typedef CGAL::cpp11::array<FT, 3> Eigen_vector;
|
||||
typedef CGAL::cpp11::array<FT, 9> Eigen_three_vectors;
|
||||
|
||||
// If Eigen is enabled, use it, otherwise fallback to the internal model
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
typedef CGAL::Eigen_diagonalize_traits<FT, 3> Diagonalize_traits;
|
||||
#else
|
||||
typedef CGAL::Internal_diagonalize_traits<FT, 3> Diagonalize_traits;
|
||||
#endif
|
||||
|
||||
int main(void)
|
||||
{
|
||||
Eigen_matrix covariance = {{ 0., 0., 0., 0., 0., 0. }};
|
||||
|
||||
// Fill matrix with random numbers
|
||||
for (std::size_t i = 0; i < 6; ++ i)
|
||||
covariance[i] = rand ();
|
||||
|
||||
Eigen_vector eigenvalues;
|
||||
Eigen_three_vectors eigenvectors;
|
||||
|
||||
if (!(Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix (covariance,
|
||||
eigenvalues,
|
||||
eigenvectors)))
|
||||
{
|
||||
std::cerr << "Error: cannot diagonalize matrix" << std::endl;
|
||||
return -1;
|
||||
}
|
||||
|
||||
// Print result
|
||||
for (std::size_t i = 0; i < 3; ++ i)
|
||||
{
|
||||
std::cout << "Eigenvalue " << i+1 << " = " << eigenvalues[i] << std::endl
|
||||
<< " with eigenvector [ ";
|
||||
for (std::size_t j = 0; j < 3; ++ j)
|
||||
std::cout << eigenvectors[3*i + j] << " ";
|
||||
std::cout << "]" << std::endl;
|
||||
}
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,44 @@
|
|||
// If Eigen is available, use it, otherwise switch to Lapack
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
#include <CGAL/Eigen_matrix.h>
|
||||
#include <CGAL/Eigen_vector.h>
|
||||
#include <CGAL/Eigen_svd.h>
|
||||
typedef CGAL::Eigen_svd Svd;
|
||||
|
||||
#else
|
||||
#ifdef CGAL_LAPACK_ENABLED
|
||||
#include <CGAL/Lapack_svd.h>
|
||||
typedef CGAL::Lapack_svd Svd;
|
||||
#endif
|
||||
#endif
|
||||
|
||||
typedef Svd::FT FT;
|
||||
typedef Svd::Vector Eigen_vector;
|
||||
typedef Svd::Matrix Eigen_matrix;
|
||||
|
||||
int main(void)
|
||||
{
|
||||
std::size_t degree = 3;
|
||||
|
||||
Eigen_vector B (degree);
|
||||
Eigen_matrix M (degree, degree);
|
||||
|
||||
// Fill B and M with random numbers
|
||||
for (std::size_t i = 0; i < degree; ++ i)
|
||||
{
|
||||
B.set (i, rand());
|
||||
for (std::size_t j = 0; j < degree; ++ j)
|
||||
M.set (i, j, rand());
|
||||
}
|
||||
|
||||
// Solve MX=B
|
||||
std::cout << Svd::solve(M, B) << std::endl;
|
||||
|
||||
// Print result
|
||||
std::cout << "Solution of SVD = [ ";
|
||||
for (std::size_t i = 0; i < degree; ++ i)
|
||||
std::cout << B.vector()[i] << " ";
|
||||
std::cout << "]" << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
#include <CGAL/Eigen_solver_traits.h>
|
||||
#include <CGAL/Eigen_matrix.h>
|
||||
|
||||
|
||||
typedef CGAL::Eigen_solver_traits<Eigen::ConjugateGradient<CGAL::Eigen_sparse_matrix<double>::EigenType> > Eigen_solver;
|
||||
typedef Eigen_solver::NT FT;
|
||||
typedef Eigen_solver::Matrix Eigen_matrix;
|
||||
typedef Eigen_solver::Vector Eigen_vector;
|
||||
|
||||
|
||||
int main(void)
|
||||
{
|
||||
srand (time (NULL));
|
||||
std::size_t degree = 3000;
|
||||
std::size_t nb_nonzero_coef = 100;
|
||||
|
||||
Eigen_vector B (degree);
|
||||
Eigen_matrix A (degree);
|
||||
|
||||
Eigen_vector diag (degree);
|
||||
|
||||
// Randomly make some coefficients of the matrix non-zero
|
||||
for (std::size_t i = 0; i < nb_nonzero_coef; ++ i)
|
||||
{
|
||||
std::size_t x = rand () % degree;
|
||||
std::size_t y = rand () % degree;
|
||||
if (x == y)
|
||||
continue;
|
||||
|
||||
FT value = rand () / static_cast<FT> (RAND_MAX);
|
||||
|
||||
A.add_coef (x, y, value);
|
||||
diag.set (x, diag.vector()[x] - value);
|
||||
|
||||
B.set (x, 1.);
|
||||
}
|
||||
|
||||
for (std::size_t i = 0; i < degree; ++ i)
|
||||
A.add_coef (i, i, diag.vector()[i]);
|
||||
|
||||
// Create sparse matrix
|
||||
A.assemble_matrix();
|
||||
|
||||
Eigen_vector X (degree);
|
||||
FT d;
|
||||
|
||||
Eigen_solver solver;
|
||||
if (!(solver.linear_solver (A, B, X, d)))
|
||||
{
|
||||
std::cerr << "Error: linear solver failed" << std::endl;
|
||||
return -1;
|
||||
}
|
||||
|
||||
// Print extract of result
|
||||
std::cout << "Vector X (non-zero coefficients) = [ ";
|
||||
for (std::size_t i = 0; i < degree; ++ i)
|
||||
if (X.vector()[i] != 0.)
|
||||
std::cout << X.vector()[i] << " ";
|
||||
std::cout << "]" << std::endl;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,58 @@
|
|||
#ifndef CGAL_DEFAULT_DIAGONALIZE_TRAITS_H
|
||||
#define CGAL_DEFAULT_DIAGONALIZE_TRAITS_H
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
#include <CGAL/Eigen_diagonalize_traits.h>
|
||||
#else
|
||||
#include <CGAL/Internal_diagonalize_traits.h>
|
||||
#endif
|
||||
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
|
||||
// Wrapper class designed to automatically use
|
||||
// Eigen_diagonalize_traits if Eigen is available and otherwise use
|
||||
// the fallback Internal_diagonalize_traits class.
|
||||
|
||||
template <typename FT, unsigned int dim = 3>
|
||||
class Default_diagonalize_traits{
|
||||
|
||||
#ifdef CGAL_EIGEN3_ENABLED
|
||||
typedef Eigen_diagonalize_traits<FT, dim> Base;
|
||||
#else
|
||||
typedef Internal_diagonalize_traits<FT, dim> Base;
|
||||
#endif
|
||||
|
||||
public:
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues)
|
||||
{
|
||||
return Base::diagonalize_selfadjoint_covariance_matrix (cov, eigenvalues);
|
||||
}
|
||||
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues,
|
||||
cpp11::array<FT, dim * dim>& eigenvectors)
|
||||
{
|
||||
return Base::diagonalize_selfadjoint_covariance_matrix (cov, eigenvalues, eigenvectors);
|
||||
}
|
||||
|
||||
// Extract the eigenvector associated to the largest eigenvalue
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT,dim> &normal)
|
||||
{
|
||||
return Base::extract_largest_eigenvector_of_covariance_matrix (cov, normal);
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
#endif // CGAL_DEFAULT_DIAGONALIZE_TRAITS_H
|
||||
|
|
@ -0,0 +1,149 @@
|
|||
// Copyright (c) 2014 INRIA Sophia-Antipolis (France).
|
||||
// All rights reserved.
|
||||
//
|
||||
// This file is part of CGAL (www.cgal.org).
|
||||
// You can redistribute it and/or modify it under the terms of the GNU
|
||||
// General Public License as published by the Free Software Foundation,
|
||||
// either version 3 of the License, or (at your option) any later version.
|
||||
//
|
||||
// Licensees holding a valid commercial license may use this file in
|
||||
// accordance with the commercial license agreement provided with the software.
|
||||
//
|
||||
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||||
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||||
//
|
||||
// $URL$
|
||||
// $Id$
|
||||
//
|
||||
// Author(s) : Jocelyn Meyron and Quentin Mérigot
|
||||
//
|
||||
|
||||
#ifndef CGAL_EIGEN_DIAGONALIZE_TRAITS_H
|
||||
#define CGAL_EIGEN_DIAGONALIZE_TRAITS_H
|
||||
|
||||
#include <Eigen/Dense>
|
||||
#include <Eigen/Eigenvalues>
|
||||
|
||||
#include <CGAL/array.h>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
/// A model of the concept `DiagonalizeTraits` using \ref thirdpartyEigen.
|
||||
/// \cgalModels `DiagonalizeTraits`
|
||||
|
||||
template <typename FT, unsigned int dim = 3>
|
||||
class Eigen_diagonalize_traits{
|
||||
|
||||
typedef Eigen::Matrix<FT, dim, dim> Matrix;
|
||||
typedef Eigen::Matrix<FT, dim, 1> Vector;
|
||||
|
||||
// Construct the covariance matrix
|
||||
static Matrix
|
||||
construct_covariance_matrix
|
||||
(const cpp11::array<FT, (dim * (dim+1) / 2)>& cov) {
|
||||
Matrix m;
|
||||
|
||||
for (std::size_t i = 0; i < dim; ++ i)
|
||||
for (std::size_t j = i; j < dim; ++ j)
|
||||
{
|
||||
m(i,j) = static_cast<float>(cov[(dim * i) + j - ((i * (i+1)) / 2)]);
|
||||
if (i != j)
|
||||
m(j,i) = m(i,j);
|
||||
}
|
||||
|
||||
return m;
|
||||
}
|
||||
|
||||
// Diagonalize a selfadjoint matrix
|
||||
static bool
|
||||
diagonalize_selfadjoint_matrix (Matrix& m,
|
||||
Matrix& eigenvectors,
|
||||
Vector& eigenvalues) {
|
||||
Eigen::SelfAdjointEigenSolver<Matrix> eigensolver(m);
|
||||
|
||||
if (eigensolver.info() != Eigen::Success) {
|
||||
return false;
|
||||
}
|
||||
|
||||
eigenvalues = eigensolver.eigenvalues();
|
||||
eigenvectors = eigensolver.eigenvectors();
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
public:
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues)
|
||||
{
|
||||
Matrix m = construct_covariance_matrix(cov);
|
||||
|
||||
// Diagonalizing the matrix
|
||||
Vector eigenvalues_;
|
||||
Matrix eigenvectors_;
|
||||
bool res = diagonalize_selfadjoint_matrix(m, eigenvectors_, eigenvalues_);
|
||||
|
||||
if (res)
|
||||
{
|
||||
for (std::size_t i = 0; i < dim; ++ i)
|
||||
eigenvalues[i] = static_cast<FT>(eigenvalues_[i]);
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix(
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues,
|
||||
cpp11::array<FT, dim * dim>& eigenvectors)
|
||||
{
|
||||
Matrix m = construct_covariance_matrix(cov);
|
||||
|
||||
// Diagonalizing the matrix
|
||||
Vector eigenvalues_;
|
||||
Matrix eigenvectors_;
|
||||
bool res = diagonalize_selfadjoint_matrix(m, eigenvectors_, eigenvalues_);
|
||||
|
||||
if (res)
|
||||
{
|
||||
for (std::size_t i = 0; i < dim; ++ i)
|
||||
{
|
||||
eigenvalues[i] = static_cast<FT>(eigenvalues_[i]);
|
||||
|
||||
for (std::size_t j = 0; j < dim; ++ j)
|
||||
eigenvectors[dim*i + j]=static_cast<FT>(eigenvectors_(j,i));
|
||||
}
|
||||
}
|
||||
|
||||
return res;
|
||||
}
|
||||
|
||||
// Extract the eigenvector associated to the largest eigenvalue
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix (
|
||||
const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT,dim> &normal)
|
||||
{
|
||||
// Construct covariance matrix
|
||||
Matrix m = construct_covariance_matrix(cov);
|
||||
|
||||
// Diagonalizing the matrix
|
||||
Vector eigenvalues;
|
||||
Matrix eigenvectors;
|
||||
if (! diagonalize_selfadjoint_matrix(m, eigenvectors, eigenvalues)) {
|
||||
return false;
|
||||
}
|
||||
|
||||
// Eigenvalues are sorted by increasing order
|
||||
for (unsigned int i = 0; i < dim; ++ i)
|
||||
normal[i] = static_cast<FT> (eigenvectors(i,dim-1));
|
||||
|
||||
return true;
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
#endif // CGAL_EIGEN_DIAGONALIZE_TRAITS_H
|
||||
|
|
@ -69,7 +69,7 @@ namespace internal {
|
|||
/// is a generic traits class for solving asymmetric or symmetric positive definite (SPD)
|
||||
/// sparse linear systems using one of the Eigen solvers.
|
||||
/// The default solver is the iterative bi-congugate gradient stabilized solver
|
||||
/// Eigen::BiCGSTAB for double.
|
||||
/// <a href="http://eigen.tuxfamily.org/dox/classEigen_1_1BiCGSTAB.html">Eigen::BiCGSTAB</a> for double.
|
||||
///
|
||||
/// \cgalModels `SparseLinearAlgebraTraitsWithFactor_d`.
|
||||
|
||||
|
|
@ -79,6 +79,7 @@ class Eigen_solver_traits
|
|||
typedef typename EigenSolverT::Scalar Scalar;
|
||||
// Public types
|
||||
public:
|
||||
typedef EigenSolverT Solver;
|
||||
typedef Scalar NT;
|
||||
typedef typename internal::Get_eigen_matrix<EigenSolverT,NT>::type Matrix;
|
||||
typedef Eigen_vector<Scalar> Vector;
|
||||
|
|
@ -159,7 +160,7 @@ protected:
|
|||
|
||||
};
|
||||
|
||||
//specilization of the solver for BiCGSTAB as for surface parameterization, the
|
||||
//specialization of the solver for BiCGSTAB as for surface parameterization, the
|
||||
//intializer should be a vector of one's (this was the case in 3.1-alpha but not in the official 3.1).
|
||||
template<>
|
||||
class Eigen_solver_traits< Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType> >
|
||||
|
|
@ -168,6 +169,7 @@ class Eigen_solver_traits< Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenTyp
|
|||
typedef EigenSolverT::Scalar Scalar;
|
||||
// Public types
|
||||
public:
|
||||
typedef EigenSolverT Solver;
|
||||
typedef Scalar NT;
|
||||
typedef internal::Get_eigen_matrix<EigenSolverT,NT>::type Matrix;
|
||||
typedef Eigen_vector<Scalar> Vector;
|
||||
|
|
|
|||
|
|
@ -0,0 +1,247 @@
|
|||
#ifndef CGAL_INTERNAL_DIAGONALIZE_TRAITS_H
|
||||
#define CGAL_INTERNAL_DIAGONALIZE_TRAITS_H
|
||||
|
||||
#include <CGAL/array.h>
|
||||
|
||||
namespace CGAL {
|
||||
|
||||
/// A model of the concept `DiagonalizeTraits`
|
||||
/// \cgalModels `DiagonalizeTraits`
|
||||
|
||||
template <typename FT, unsigned int dim = 3>
|
||||
class Internal_diagonalize_traits{
|
||||
|
||||
public:
|
||||
static bool
|
||||
diagonalize_selfadjoint_covariance_matrix
|
||||
(const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT, dim>& eigenvalues)
|
||||
{
|
||||
cpp11::array<FT, dim * dim> eigenvectors;
|
||||
return diagonalize_selfadjoint_covariance_matrix (cov, eigenvalues, eigenvectors);
|
||||
}
|
||||
|
||||
// Extract the eigenvector associated to the largest eigenvalue
|
||||
static bool
|
||||
extract_largest_eigenvector_of_covariance_matrix
|
||||
(const cpp11::array<FT, (dim * (dim+1) / 2)>& cov,
|
||||
cpp11::array<FT,dim> &normal)
|
||||
{
|
||||
cpp11::array<FT, dim> eigenvalues;
|
||||
cpp11::array<FT, dim * dim> eigenvectors;
|
||||
|
||||
diagonalize_selfadjoint_covariance_matrix (cov, eigenvalues, eigenvectors);
|
||||
|
||||
for (std::size_t i = 0; i < dim; ++ i)
|
||||
normal[i] = static_cast<FT> (eigenvectors[(dim*(dim-1))+i]);
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
static bool diagonalize_selfadjoint_covariance_matrix
|
||||
(const cpp11::array<FT, (dim * (dim+1) / 2)>& mat,
|
||||
cpp11::array<FT, dim>& eigen_values,
|
||||
cpp11::array<FT, dim * dim>& eigen_vectors)
|
||||
{
|
||||
const int n = dim;
|
||||
|
||||
const int MAX_ITER = 100;
|
||||
static const FT EPSILON = (FT)0.00001;
|
||||
|
||||
// number of entries in mat
|
||||
int nn = (n*(n+1))/2;
|
||||
|
||||
// copy matrix
|
||||
FT *a = new FT[nn];
|
||||
int ij;
|
||||
|
||||
// This function requires lower triangular, so we switch
|
||||
for (int i = 0; i < n; ++ i)
|
||||
for (int j = i; j < n; ++ j)
|
||||
a[(n * i) + j - ((i * (i+1)) / 2)]
|
||||
= mat[i + (j * (j+1) / 2)];
|
||||
|
||||
// Fortran-porting
|
||||
a--;
|
||||
|
||||
// init diagonalization matrix as the unit matrix
|
||||
FT *v = new FT[n*n];
|
||||
ij = 0;
|
||||
int i;
|
||||
for(i=0; i<n; i++)
|
||||
for(int j=0; j<n; j++)
|
||||
if(i==j)
|
||||
v[ij++] = 1.0;
|
||||
else
|
||||
v[ij++] = 0.0;
|
||||
// Fortran-porting
|
||||
v--;
|
||||
|
||||
// compute weight of the non diagonal terms
|
||||
ij = 1;
|
||||
FT a_norm = 0.0;
|
||||
for(i=1; i<=n; i++)
|
||||
for(int j=1; j<=i; j++)
|
||||
{
|
||||
if( i!=j )
|
||||
{
|
||||
FT a_ij = a[ij];
|
||||
a_norm += a_ij * a_ij;
|
||||
}
|
||||
ij++;
|
||||
}
|
||||
|
||||
if(a_norm != 0.0)
|
||||
{
|
||||
FT a_normEPS = a_norm * EPSILON;
|
||||
FT thr = a_norm;
|
||||
|
||||
// rotations
|
||||
int nb_iter = 0;
|
||||
while(thr > a_normEPS && nb_iter < MAX_ITER)
|
||||
{
|
||||
nb_iter++;
|
||||
FT thr_nn = thr / nn;
|
||||
|
||||
for(int l=1; l< n; l++)
|
||||
{
|
||||
for(int m=l+1; m<=n; m++)
|
||||
{
|
||||
// compute sinx and cosx
|
||||
int lq = (l*l-l)/2;
|
||||
int mq = (m*m-m)/2;
|
||||
|
||||
int lm = l + mq;
|
||||
FT a_lm = a[lm];
|
||||
FT a_lm_2 = a_lm * a_lm;
|
||||
|
||||
if(a_lm_2 < thr_nn)
|
||||
continue;
|
||||
|
||||
int ll = l + lq;
|
||||
int mm = m + mq;
|
||||
FT a_ll = a[ll];
|
||||
FT a_mm = a[mm];
|
||||
|
||||
FT delta = a_ll - a_mm;
|
||||
|
||||
FT x;
|
||||
if(delta == 0.0)
|
||||
x = (FT) - CGAL_PI / 4;
|
||||
else
|
||||
x = (FT)(- std::atan( (a_lm+a_lm) / delta ) / 2.0);
|
||||
|
||||
FT sinx = std::sin(x);
|
||||
FT cosx = std::cos(x);
|
||||
FT sinx_2 = sinx * sinx;
|
||||
FT cosx_2 = cosx * cosx;
|
||||
FT sincos = sinx * cosx;
|
||||
|
||||
// rotate L and M columns
|
||||
int ilv = n*(l-1);
|
||||
int imv = n*(m-1);
|
||||
|
||||
int i;
|
||||
for( i=1; i<=n;i++ )
|
||||
{
|
||||
if( (i!=l) && (i!=m) )
|
||||
{
|
||||
int iq = (i*i-i)/2;
|
||||
|
||||
int im;
|
||||
if( i<m )
|
||||
im = i + mq;
|
||||
else
|
||||
im = m + iq;
|
||||
FT a_im = a[im];
|
||||
|
||||
int il;
|
||||
if( i<l )
|
||||
il = i + lq;
|
||||
else
|
||||
il = l + iq;
|
||||
FT a_il = a[il];
|
||||
|
||||
a[il] = a_il * cosx - a_im * sinx;
|
||||
a[im] = a_il * sinx + a_im * cosx;
|
||||
}
|
||||
|
||||
ilv++;
|
||||
imv++;
|
||||
|
||||
FT v_ilv = v[ilv];
|
||||
FT v_imv = v[imv];
|
||||
|
||||
v[ilv] = cosx * v_ilv - sinx * v_imv;
|
||||
v[imv] = sinx * v_ilv + cosx * v_imv;
|
||||
}
|
||||
|
||||
x = a_lm * sincos;
|
||||
x += x;
|
||||
|
||||
a[ll] = a_ll * cosx_2 + a_mm * sinx_2 - x;
|
||||
a[mm] = a_ll * sinx_2 + a_mm * cosx_2 + x;
|
||||
a[lm] = 0.0;
|
||||
|
||||
thr = CGAL::abs(thr - a_lm_2);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// convert indices and copy eigen values
|
||||
a++;
|
||||
for(i=0; i<n; i++)
|
||||
{
|
||||
int k = i + (i*(i+1))/2;
|
||||
eigen_values[i] = a[k];
|
||||
}
|
||||
delete [] a;
|
||||
|
||||
// sort eigen values and vectors
|
||||
int *index = new int[n];
|
||||
for(i=0; i<n; i++)
|
||||
index[i] = i;
|
||||
|
||||
for(i=0; i<(n-1); i++)
|
||||
{
|
||||
FT x = eigen_values[i];
|
||||
int k = i;
|
||||
|
||||
for(int j=i+1; j<n; j++)
|
||||
if(x > eigen_values[j])
|
||||
{
|
||||
k = j;
|
||||
x = eigen_values[j];
|
||||
}
|
||||
|
||||
eigen_values[k] = eigen_values[i];
|
||||
eigen_values[i] = x;
|
||||
|
||||
int jj = index[k];
|
||||
index[k] = index[i];
|
||||
index[i] = jj;
|
||||
}
|
||||
|
||||
|
||||
// save eigen vectors
|
||||
v++; // back to C++
|
||||
ij = 0;
|
||||
for(int k=0; k<n; k++ )
|
||||
{
|
||||
int ik = index[k]*n;
|
||||
for(int i=0; i<n; i++)
|
||||
eigen_vectors[ij++] = v[ik++];
|
||||
}
|
||||
|
||||
delete [] v;
|
||||
delete [] index;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
||||
#endif // CGAL_INTERNAL_DIAGONALIZE_TRAITS_H
|
||||
|
|
@ -12,7 +12,7 @@
|
|||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.2}
|
||||
\cgalPkgDependsOn{Solvers as \ref thirdpartyEigen.}
|
||||
\cgalPkgDependsOn{\ref PkgSolverSummary}
|
||||
\cgalPkgBib{cgal:sal-pptsm2}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgDemo{Operations on Polyhedra,polyhedron_3.zip}
|
||||
|
|
@ -31,7 +31,6 @@
|
|||
- `BorderParameterizer_3`
|
||||
- `ParameterizationMesh_3`
|
||||
- `ParameterizationPatchableMesh_3`
|
||||
- `SparseLinearAlgebraTraits_d`
|
||||
- `PolyhedronTraitsWithKernel_3`
|
||||
|
||||
## Surface Parameterization Methods ##
|
||||
|
|
@ -55,7 +54,7 @@ This \cgal package implements several parameterization methods:
|
|||
- `CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
- `CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
- `CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
- `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
- `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3>`
|
||||
- `CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
|
||||
## Border Parameterization Methods ##
|
||||
|
|
@ -122,16 +121,6 @@ The package provides an interface with `CGAL::Polyhedron_3<Traits>`:
|
|||
|
||||
A `(u,v)` pair is computed for each inner vertex (i.e.\ its halfedges share the same `(u,v)` pair), while a `(u,v)` pair is computed for each border halfedge. The user must iterate over the mesh halfedges to get the result.
|
||||
|
||||
## Sparse Linear Algebra ##
|
||||
|
||||
Since parameterizing meshes requires
|
||||
efficient representation of sparse matrices and efficient iterative or
|
||||
direct linear solvers, we provide an interface to several
|
||||
sparse linear solvers:
|
||||
- <span class="textsc">Eigen</span> 3.1 (or greater) is the library recommended by %CGAL solving sparse systems.
|
||||
- OpenNL (authored by Bruno Lévy) is shipped with %CGAL is the default solver.
|
||||
- `OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
|
||||
- `OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
|
||||
|
||||
## Helper Classes ##
|
||||
|
||||
|
|
@ -250,18 +239,6 @@ The package provides an interface with `CGAL::Polyhedron_3<Traits>`:
|
|||
|
||||
|
||||
|
||||
/*! \defgroup PkgSurfaceParameterizationAlgebra Sparse Linear Algebra
|
||||
\ingroup PkgSurfaceParameterization
|
||||
|
||||
Since parameterizing meshes requires
|
||||
efficient representation of sparse matrices and efficient iterative or
|
||||
direct linear solvers, we provide an interface to several
|
||||
sparse linear solvers:
|
||||
- <span class="textsc">Eigen</span> 3.1 (or greater) is the library recommended by %CGAL solving sparse systems.
|
||||
- OpenNL (authored by Bruno Lévy) is shipped with %CGAL is the default solver.
|
||||
- `OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
|
||||
- `OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
|
||||
*/
|
||||
|
||||
/*!
|
||||
\defgroup PkgSurfaceParameterizationHelper Helper Class
|
||||
|
|
|
|||
|
|
@ -40,9 +40,8 @@ data structure.
|
|||
|
||||
Since parameterizing meshes require efficient representation of sparse
|
||||
matrices and efficient iterative or direct linear solvers, we provide
|
||||
a unified interface to a linear solver library (\ref thirdpartyEigen "Eigen"),
|
||||
and propose a separate package devoted to OpenNL sparse
|
||||
linear solver.
|
||||
a unified interface to linear solvers as described in Chapter
|
||||
\ref PkgSolverSummary.
|
||||
|
||||
Note that linear solvers commonly use double precision floating point
|
||||
numbers. Therefore, this package is intended to be used with a \cgal %Cartesian kernel with doubles.
|
||||
|
|
@ -69,8 +68,8 @@ Parameterizer_traits_3<ParameterizationMesh_3>::Error_code parameterize (Paramet
|
|||
|
||||
The function `parameterize()` applies a default surface parameterization
|
||||
method, namely Floater Mean Value Coordinates \cgalCite{cgal:f-mvc-03}, with an
|
||||
arc-length circular border parameterization, and using OpenNL sparse
|
||||
linear solver \cgalCite{cgal:l-nmdgp-05}. The `ParameterizationMesh_3` concept defines the input meshes handled by `parameterize()`. See Section \ref secInputMeshforparameterize. The result is stored into the `(u,v)` fields of the mesh halfedges.
|
||||
arc-length circular border parameterization, and using a sparse
|
||||
linear solver from the \ref thirdpartyEigen library. The `ParameterizationMesh_3` concept defines the input meshes handled by `parameterize()`. See Section \ref secInputMeshforparameterize. The result is stored into the `(u,v)` fields of the mesh halfedges.
|
||||
The mesh must be a triangle mesh surface with one connected component.
|
||||
|
||||
Note: `Parameterizer_traits_3<ParameterizationMesh_3>` is the (pure virtual) superclass of all surface parameterizations and defines the error codes.
|
||||
|
|
@ -155,7 +154,7 @@ and \ref secBorderParameterizationsforFreeMethods.
|
|||
\subsection Surface_mesh_parameterizationTheSparseLinearAlgebraTraitsd The SparseLinearAlgebraTraits_d Concept
|
||||
|
||||
This package solves sparse linear systems using solvers which are models
|
||||
of `SparseLinearAlgebraTraits_d`. See Section \ref secSparseLinearAlgebra.
|
||||
of `SparseLinearAlgebraTraits_d`. See Chapter \ref PkgSolverSummary.
|
||||
|
||||
\subsection Surface_mesh_parameterizationTheParameterizationMesh3 The ParameterizationMesh_3 and ParameterizationPatchableMesh_3 Concepts
|
||||
|
||||
|
|
@ -419,65 +418,7 @@ Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer()
|
|||
|
||||
\endcode
|
||||
|
||||
\section secSparseLinearAlgebra Sparse Linear Algebra
|
||||
|
||||
Parameterizing triangle meshes requires both efficient representation
|
||||
of sparse matrices and efficient iterative or direct linear
|
||||
solvers. We provide links to \ref thirdpartyEigen "Eigen" library
|
||||
and include a separate package devoted to OpenNL sparse linear solver.
|
||||
|
||||
\subsection Surface_mesh_parameterizationListofSolvers List of Solvers
|
||||
|
||||
We provide an interface to several sparse linear solvers, as models
|
||||
of the `SparseLinearAlgebraTraits_d` concept:
|
||||
|
||||
- An interface to sparse solvers from the `OpenNL` library \cgalCite{cgal:l-nmdgp-05} is provided through classes
|
||||
`OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` and
|
||||
`OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>`. The OpenNL library version shipped with \cgal is a lightweight default sparse linear solver. It does not support large systems, but it is portable and
|
||||
supports exact number types.
|
||||
|
||||
- An interface to all sparse solvers from the \ref thirdpartyEigen "Eigen" library is provided through the class
|
||||
`Eigen_solver_traits<T>`. This solver traits class can be used for an iterative or a direct,
|
||||
symmetric or general sparse solvers. The \ref thirdpartyEigen "Eigen" solver to be used must be given as template parameter.
|
||||
|
||||
\subsection Surface_mesh_parameterizationEigenSolver Eigen Solver Example
|
||||
|
||||
The example \ref Surface_mesh_parameterization/Eigen_parameterization.cpp "Eigen_parameterization.cpp" computes the
|
||||
default parameterization method (Floater mean value coordinates with a circular border),
|
||||
but specifically instantiates an \ref thirdpartyEigen "Eigen" solver. Specifying a specific solver
|
||||
instead of the default one (OpenNL) means using the third parameter of
|
||||
`Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`. The differences with the first
|
||||
example \ref Surface_mesh_parameterization/Simple_parameterization.cpp "Simple_parameterization.cpp" are:
|
||||
|
||||
\code{.cpp}
|
||||
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
...
|
||||
|
||||
//***************************************
|
||||
// Floater Mean Value Coordinates parameterization
|
||||
// (circular border) with Eigen solver
|
||||
//***************************************
|
||||
|
||||
// Circular border parameterizer (the default)
|
||||
typedef CGAL::Circular_border_arc_length_parameterizer_3<Parameterization_polyhedron_adaptor>
|
||||
Border_parameterizer;
|
||||
// Eigen solver
|
||||
typedef CGAL::Eigen_solver_traits<> Solver;
|
||||
|
||||
// Floater Mean Value Coordinates parameterization
|
||||
// (circular border) with Eigen solver
|
||||
typedef CGAL::Mean_value_coordinates_parameterizer_3<Parameterization_polyhedron_adaptor,
|
||||
Border_parameterizer,
|
||||
Solver>
|
||||
Parameterizer;
|
||||
|
||||
Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer());
|
||||
|
||||
...
|
||||
|
||||
\endcode
|
||||
|
||||
\section secCuttingaMesh Cutting a Mesh
|
||||
|
||||
|
|
@ -605,63 +546,7 @@ and is therefore non-singular (Gram theorem).
|
|||
|
||||
</UL>
|
||||
|
||||
\subsection Surface_mesh_parameterizationPrecision Precision
|
||||
|
||||
Two algorithms of this package construct the sparse linear system(s)
|
||||
using trigonometric functions, and are this incompatible with exact arithmetic:
|
||||
|
||||
<UL>
|
||||
|
||||
<LI>Floater mean value coordinates
|
||||
|
||||
<LI>Circular border parameterization
|
||||
|
||||
</UL>
|
||||
|
||||
On the other hand, linear solvers commonly use double precision floating point
|
||||
numbers.
|
||||
|
||||
OpenNL's BICGSTAB solver (accessible through the
|
||||
`OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` interface)
|
||||
is the only solver supported by this package which
|
||||
computes exact results, when used with an exact arithmetic. This package is
|
||||
intended to be used mainly with a \cgal %Cartesian kernel with doubles.
|
||||
|
||||
\subsection Surface_mesh_parameterizationOpenNLsBICGSTAB OpenNL's BICGSTAB Solver with an Exact Arithmetic
|
||||
|
||||
The BICGSTAB conjugate gradient is in disguise a direct solver.
|
||||
In a nutshell, it computes a vector basis
|
||||
orthogonal with respect to the matrix, and the coordinates of the solution in this vector basis.
|
||||
Each iteration computes one component of the basis and one coordinate, therefore the algorithm
|
||||
converges to the solution in \f$ n\f$ iterations, where \f$ n\f$ is the dimension of the matrix. More precisely, it is shown to converge in \f$ k\f$ iteration, where \f$ k\f$ is the number of distinct eigenvalues of the matrix.
|
||||
|
||||
\subsection Surface_mesh_parameterizationSolverswith Solvers with a Floating Point Arithmetic
|
||||
|
||||
<I>OpenNL's BICGSTAB example:</I>
|
||||
|
||||
When inexact numerical types are used (e.g. doubles), accumulated errors slow down convergence
|
||||
(in practice, it requires approximately \f$ 5k\f$ iterations to converge).
|
||||
The required number of iterations depends on the eigenvalues of the matrix, and these eigenvalues depend
|
||||
on the shape of the triangles. The optimum is when the triangles are equilateral (then the solver converges
|
||||
in less than 10 iterations). The worst case is obtained when the mesh has a large number of skinny triangles (near-singular Jacobian matrix of the triangle). In this case, the spectrum of the matrix
|
||||
is wide (many different eigenvalues), and the solver requires nearly \f$ 5n\f$ iterations to converge.
|
||||
|
||||
\subsection Surface_mesh_parameterizationAlgorithmic Algorithmic Complexity
|
||||
|
||||
In this package, we focus on piecewise linear mappings onto a planar
|
||||
domain. All surface parameterization methods are based on solving one (or two)
|
||||
sparse linear system(s).
|
||||
The algorithmic complexity is dominated by the resolution of the sparse linear system(s).
|
||||
|
||||
<I>OpenNL's BICGSTAB example:</I>
|
||||
|
||||
At each iteration, the operation of highest complexity is the product between the sparse-matrix and a vector.
|
||||
The sparse matrix has a fixed number of non-zero coefficients per row,
|
||||
therefore the matrix / vector product has \f$ O(n)\f$ complexity.
|
||||
Since convergence is reached after \f$ k\f$ iterations, the complexity is \f$ O(k.n)\f$
|
||||
(where \f$ k\f$ is the number of distinct eigenvalues of the matrix).
|
||||
Therefore, best case complexity is \f$ O(n)\f$ (equilateral triangles),
|
||||
and worst case complexity is \f$ O(n^2)\f$ (skinny triangles).
|
||||
|
||||
\section Surface_mesh_parameterizationSoftware Software Design
|
||||
|
||||
|
|
@ -801,7 +686,7 @@ The purpose of such a model is to:
|
|||
<LI>Support several kind of meshes.
|
||||
<LI>Hide the implementation of extra fields specific to the parameterization domain
|
||||
(`index`, `u`, `v`, `is_parameterized`).
|
||||
<LI>Handle in the mesh type the complexity of <I>virtually</I> cutting a mesh
|
||||
<LI>%Handle in the mesh type the complexity of <I>virtually</I> cutting a mesh
|
||||
to make it homeomorphic to a disk (instead of duplicating this
|
||||
code in each parameterization method).
|
||||
</OL>
|
||||
|
|
@ -834,15 +719,6 @@ This mainly means that:
|
|||
can be set <I>per corner</I> (which is a more general way of saying <I>per half-edge</I>).
|
||||
</UL>
|
||||
|
||||
\subsection Surface_mesh_parameterizationSparseLinearAlgebraTraitsd SparseLinearAlgebraTraits_d Concept
|
||||
|
||||
This package solves sparse linear systems using solvers which are models
|
||||
of `SparseLinearAlgebraTraits_d`.
|
||||
|
||||
`SparseLinearAlgebraTraits_d` is a sub-concept of the `LinearAlgebraTraits_d` concept
|
||||
in `Kernel_d`.
|
||||
The goal is to adapt easily code written for dense matrices to sparse ones,
|
||||
and vice-versa.
|
||||
|
||||
\subsection Surface_mesh_parameterizationCuttingaMesh_1 Cutting a Mesh
|
||||
|
||||
|
|
@ -855,23 +731,7 @@ not intend to cover this topic at the moment.
|
|||
|
||||
\section Surface_mesh_parameterizationExtendingthe Extending the Package and Reusing Code
|
||||
|
||||
\subsection Surface_mesh_parameterizationReusingMesh Reusing Mesh Adaptors
|
||||
|
||||
`ParameterizationMesh_3` defines a concept to access to a
|
||||
general polyhedral mesh.
|
||||
It is optimized for the `Surface_mesh_parameterization` package
|
||||
only in the sense that it
|
||||
defines the accessors to fields specific to the parameterization domain
|
||||
(`index`, `u`, `v`, `is_parameterized`).
|
||||
|
||||
It may be easily generalized.
|
||||
|
||||
\subsection Surface_mesh_parameterizationReusingSparse Reusing Sparse Linear Algebra
|
||||
|
||||
The `SparseLinearAlgebraTraits_d` concept and the traits classes
|
||||
for \ref thirdpartyEigen "Eigen" and OpenNL are independent of the rest of the
|
||||
`Surface_mesh_parameterization` package, and may be reused by
|
||||
\cgal developers for other purposes.
|
||||
|
||||
\subsection Surface_mesh_parameterizationAddingNewParameterization Adding New Parameterization Methods
|
||||
|
||||
|
|
@ -900,6 +760,7 @@ Square, circular and two-points border parameterizations are good starting point
|
|||
Obviously, this package would benefit of having robust algorithms
|
||||
which transform arbitrary meshes into topological disks.
|
||||
|
||||
|
||||
*/
|
||||
} /* namespace CGAL */
|
||||
|
||||
|
|
|
|||
|
|
@ -8,3 +8,6 @@ Polyhedron
|
|||
Kernel_d
|
||||
Surface_modeling
|
||||
Surface_mesh_skeletonization
|
||||
Solver_interface
|
||||
Convex_hull_2
|
||||
|
||||
|
|
|
|||
|
|
@ -1,5 +1,6 @@
|
|||
/// \example Surface_mesh_parameterization/Simple_parameterization.cpp
|
||||
/// \example Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp
|
||||
/// \example Surface_mesh_parameterization/Complete_parameterization_example.cpp
|
||||
/// \example Surface_mesh_parameterization/Eigen_parameterization.cpp
|
||||
/// \example Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp
|
||||
/*!
|
||||
\example Surface_mesh_parameterization/Simple_parameterization.cpp
|
||||
\example Surface_mesh_parameterization/Mesh_cutting_parameterization.cpp
|
||||
\example Surface_mesh_parameterization/Complete_parameterization_example.cpp
|
||||
\example Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -27,7 +27,6 @@ int main(int argc, char * argv[])
|
|||
std::cerr << "PARAMETERIZATION" << std::endl;
|
||||
std::cerr << " Discrete Authalic Parameterization" << std::endl;
|
||||
std::cerr << " circle border" << std::endl;
|
||||
std::cerr << " OpenNL solver" << std::endl;
|
||||
|
||||
//***************************************
|
||||
// decode parameters
|
||||
|
|
@ -68,7 +67,7 @@ int main(int argc, char * argv[])
|
|||
|
||||
//***************************************
|
||||
// Discrete Authalic Parameterization
|
||||
// (defaults are circular border and OpenNL solver)
|
||||
// (defaults are circular border and Eigen solver)
|
||||
//***************************************
|
||||
|
||||
typedef CGAL::Discrete_authalic_parameterizer_3<Parameterization_polyhedron_adaptor>
|
||||
|
|
|
|||
|
|
@ -62,25 +62,25 @@ if ( CGAL_FOUND )
|
|||
list(APPEND CGAL_3RD_PARTY_LIBRARIES ${Boost_PROGRAM_OPTIONS_LIBRARY})
|
||||
endif()
|
||||
|
||||
# Executables that do *not* require Eigen
|
||||
|
||||
find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
|
||||
|
||||
if (EIGEN3_FOUND)
|
||||
# Executables that require Eigen 3.1
|
||||
include( ${EIGEN3_USE_FILE} )
|
||||
create_single_source_cgal_program( "Authalic_parameterization.cpp" )
|
||||
create_single_source_cgal_program( "Mesh_cutting_parameterization.cpp" )
|
||||
create_single_source_cgal_program( "Simple_parameterization.cpp" )
|
||||
create_single_source_cgal_program( "Square_border_parameterization.cpp" )
|
||||
|
||||
find_package(Eigen3 3.1.0) #(requires 3.1.0 or greater)
|
||||
|
||||
if (EIGEN3_FOUND)
|
||||
# Executables that require Eigen 3.1
|
||||
include( ${EIGEN3_USE_FILE} )
|
||||
create_single_source_cgal_program( "Complete_parameterization_example.cpp" )
|
||||
create_single_source_cgal_program( "Eigen_parameterization.cpp" )
|
||||
|
||||
create_single_source_cgal_program( "polyhedron_ex_parameterization.cpp" )
|
||||
|
||||
else(EIGEN3_FOUND)
|
||||
message(STATUS "NOTICE: Some examples require Eigen 3.1 (or greater) and will not be compiled.")
|
||||
endif(EIGEN3_FOUND)
|
||||
|
||||
create_single_source_cgal_program( "polyhedron_ex_parameterization.cpp" )
|
||||
|
||||
else()
|
||||
|
||||
message(STATUS "NOTICE: This program requires the CGAL library, and will not be compiled.")
|
||||
|
|
|
|||
|
|
@ -248,14 +248,10 @@ int main(int argc, char * argv[])
|
|||
// Border parameterizer
|
||||
typedef CGAL::Square_border_arc_length_parameterizer_3<Mesh_patch_polyhedron>
|
||||
Border_parameterizer;
|
||||
// Eigen solver
|
||||
typedef CGAL::Eigen_solver_traits<> Solver;
|
||||
|
||||
// Discrete Authalic Parameterization (square border)
|
||||
// with Eigen solver
|
||||
typedef CGAL::Discrete_authalic_parameterizer_3<Mesh_patch_polyhedron,
|
||||
Border_parameterizer,
|
||||
Solver> Parameterizer;
|
||||
Border_parameterizer> Parameterizer;
|
||||
|
||||
Parameterizer::Error_code err = CGAL::parameterize(mesh_patch, Parameterizer());
|
||||
switch(err) {
|
||||
|
|
|
|||
|
|
@ -1 +0,0 @@
|
|||
data/mannequin-devil.off
|
||||
|
|
@ -1,124 +0,0 @@
|
|||
#include <CGAL/Simple_cartesian.h>
|
||||
#include <CGAL/Polyhedron_3.h>
|
||||
#include <CGAL/IO/Polyhedron_iostream.h>
|
||||
#include <CGAL/Parameterization_polyhedron_adaptor_3.h>
|
||||
#include <CGAL/parameterize.h>
|
||||
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
#include <iostream>
|
||||
#include <fstream>
|
||||
#include <cstdlib>
|
||||
|
||||
|
||||
// ----------------------------------------------------------------------------
|
||||
// Private types
|
||||
// ----------------------------------------------------------------------------
|
||||
|
||||
typedef CGAL::Simple_cartesian<double> Kernel;
|
||||
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
|
||||
|
||||
|
||||
// ----------------------------------------------------------------------------
|
||||
// main()
|
||||
// ----------------------------------------------------------------------------
|
||||
|
||||
int main(int argc, char * argv[])
|
||||
{
|
||||
std::cerr << "PARAMETERIZATION" << std::endl;
|
||||
std::cerr << " Floater parameterization" << std::endl;
|
||||
std::cerr << " Circle border" << std::endl;
|
||||
std::cerr << " Eigen solver" << std::endl;
|
||||
|
||||
//***************************************
|
||||
// decode parameters
|
||||
//***************************************
|
||||
|
||||
if (argc-1 != 1)
|
||||
{
|
||||
std::cerr << "Usage: " << argv[0] << " input_file.off" << std::endl;
|
||||
return(EXIT_FAILURE);
|
||||
}
|
||||
|
||||
// File name is:
|
||||
const char* input_filename = argv[1];
|
||||
|
||||
//***************************************
|
||||
// Read the mesh
|
||||
//***************************************
|
||||
|
||||
// Read the mesh
|
||||
std::ifstream stream(input_filename);
|
||||
Polyhedron mesh;
|
||||
stream >> mesh;
|
||||
if(!stream || !mesh.is_valid() || mesh.empty())
|
||||
{
|
||||
std::cerr << "Error: cannot read OFF file " << input_filename << std::endl;
|
||||
return EXIT_FAILURE;
|
||||
}
|
||||
|
||||
//***************************************
|
||||
// Create Polyhedron adaptor
|
||||
// Note: no cutting => we support only
|
||||
// meshes that are topological disks
|
||||
//***************************************
|
||||
|
||||
typedef CGAL::Parameterization_polyhedron_adaptor_3<Polyhedron>
|
||||
Parameterization_polyhedron_adaptor;
|
||||
|
||||
Parameterization_polyhedron_adaptor mesh_adaptor(mesh);
|
||||
|
||||
//***************************************
|
||||
// Floater Mean Value Coordinates parameterization
|
||||
// (circular border) with Eigen solver
|
||||
//***************************************
|
||||
|
||||
// Circular border parameterizer (the default)
|
||||
typedef CGAL::Circular_border_arc_length_parameterizer_3<Parameterization_polyhedron_adaptor>
|
||||
Border_parameterizer;
|
||||
// Eigen solver
|
||||
typedef CGAL::Eigen_solver_traits<> Solver;
|
||||
|
||||
// Floater Mean Value Coordinates parameterization
|
||||
// (circular border) with Eigen solver
|
||||
typedef CGAL::Mean_value_coordinates_parameterizer_3<Parameterization_polyhedron_adaptor,
|
||||
Border_parameterizer,
|
||||
Solver>
|
||||
Parameterizer;
|
||||
|
||||
Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer());
|
||||
|
||||
switch(err) {
|
||||
case Parameterizer::OK: // Success
|
||||
break;
|
||||
case Parameterizer::ERROR_EMPTY_MESH: // Input mesh not supported
|
||||
case Parameterizer::ERROR_NON_TRIANGULAR_MESH:
|
||||
case Parameterizer::ERROR_NO_TOPOLOGICAL_DISC:
|
||||
case Parameterizer::ERROR_BORDER_TOO_SHORT:
|
||||
std::cerr << "Input mesh not supported: " << Parameterizer::get_error_message(err) << std::endl;
|
||||
return EXIT_FAILURE;
|
||||
break;
|
||||
default: // Error
|
||||
std::cerr << "Error: " << Parameterizer::get_error_message(err) << std::endl;
|
||||
return EXIT_FAILURE;
|
||||
break;
|
||||
};
|
||||
|
||||
//***************************************
|
||||
// Output
|
||||
//***************************************
|
||||
|
||||
// Raw output: dump (u,v) pairs
|
||||
Polyhedron::Vertex_const_iterator pVertex;
|
||||
for (pVertex = mesh.vertices_begin();
|
||||
pVertex != mesh.vertices_end();
|
||||
pVertex++)
|
||||
{
|
||||
// (u,v) pair is stored in any halfedge
|
||||
double u = mesh_adaptor.info(pVertex->halfedge())->uv().x();
|
||||
double v = mesh_adaptor.info(pVertex->halfedge())->uv().y();
|
||||
std::cout << "(u,v) = (" << u << "," << v << ")" << std::endl;
|
||||
}
|
||||
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
|
@ -93,7 +93,6 @@ int main(int argc, char * argv[])
|
|||
std::cerr << "PARAMETERIZATION" << std::endl;
|
||||
std::cerr << " Floater parameterization" << std::endl;
|
||||
std::cerr << " Circle border" << std::endl;
|
||||
std::cerr << " OpenNL solver" << std::endl;
|
||||
std::cerr << " Very simple cut if model is not a topological disk" << std::endl;
|
||||
|
||||
//***************************************
|
||||
|
|
|
|||
|
|
@ -25,7 +25,6 @@ int main(int argc, char * argv[])
|
|||
std::cerr << "PARAMETERIZATION" << std::endl;
|
||||
std::cerr << " Floater parameterization" << std::endl;
|
||||
std::cerr << " Circle border" << std::endl;
|
||||
std::cerr << " OpenNL solver" << std::endl;
|
||||
|
||||
//***************************************
|
||||
// decode parameters
|
||||
|
|
@ -66,7 +65,7 @@ int main(int argc, char * argv[])
|
|||
|
||||
//***************************************
|
||||
// Floater Mean Value Coordinates parameterization
|
||||
// (defaults are circular border and OpenNL solver)
|
||||
// (defaults are circular border and Eigen solver)
|
||||
//***************************************
|
||||
|
||||
typedef CGAL::Parameterizer_traits_3<Parameterization_polyhedron_adaptor>
|
||||
|
|
|
|||
|
|
@ -26,7 +26,6 @@ int main(int argc, char * argv[])
|
|||
std::cerr << "PARAMETERIZATION" << std::endl;
|
||||
std::cerr << " Floater parameterization" << std::endl;
|
||||
std::cerr << " square border" << std::endl;
|
||||
std::cerr << " OpenNL solver" << std::endl;
|
||||
|
||||
//***************************************
|
||||
// decode parameters
|
||||
|
|
|
|||
|
|
@ -24,6 +24,7 @@
|
|||
|
||||
#include <CGAL/Fixed_border_parameterizer_3.h>
|
||||
#include <CGAL/surface_mesh_parameterization_assertions.h>
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
/// \file Barycentric_mapping_parameterizer_3.h
|
||||
|
||||
|
|
@ -58,7 +59,7 @@ namespace CGAL {
|
|||
\sa `CGAL::Fixed_border_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
\sa `CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
\sa `CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
\sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
\sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3>`
|
||||
\sa `CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
*/
|
||||
|
||||
|
|
@ -68,7 +69,7 @@ template
|
|||
class BorderParameterizer_3
|
||||
= Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
|
||||
class SparseLinearAlgebraTraits_d
|
||||
= OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>
|
||||
= Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >
|
||||
>
|
||||
class Barycentric_mapping_parameterizer_3
|
||||
: public Fixed_border_parameterizer_3<ParameterizationMesh_3,
|
||||
|
|
|
|||
|
|
@ -24,6 +24,7 @@
|
|||
|
||||
#include <CGAL/Fixed_border_parameterizer_3.h>
|
||||
#include <CGAL/surface_mesh_parameterization_assertions.h>
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
/// \file Discrete_authalic_parameterizer_3.h
|
||||
|
||||
|
|
@ -55,7 +56,7 @@ namespace CGAL {
|
|||
/// \sa `CGAL::Fixed_border_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3>`
|
||||
/// \sa `CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
|
||||
template
|
||||
|
|
@ -64,7 +65,7 @@ template
|
|||
class BorderParameterizer_3 ///< Strategy to parameterize the surface border
|
||||
= Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
|
||||
class SparseLinearAlgebraTraits_d ///< Traits class to solve a sparse linear system
|
||||
= OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>
|
||||
= Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >
|
||||
>
|
||||
class Discrete_authalic_parameterizer_3
|
||||
: public Fixed_border_parameterizer_3<ParameterizationMesh_3,
|
||||
|
|
|
|||
|
|
@ -24,6 +24,7 @@
|
|||
|
||||
#include <CGAL/Fixed_border_parameterizer_3.h>
|
||||
#include <CGAL/surface_mesh_parameterization_assertions.h>
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
/// \file Discrete_conformal_map_parameterizer_3.h
|
||||
|
||||
|
|
@ -61,7 +62,7 @@ namespace CGAL {
|
|||
/// \sa `CGAL::Fixed_border_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3>`
|
||||
/// \sa `CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
|
||||
template
|
||||
|
|
@ -70,7 +71,7 @@ template
|
|||
class BorderParameterizer_3
|
||||
= Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
|
||||
class SparseLinearAlgebraTraits_d
|
||||
= OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>
|
||||
= Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >
|
||||
>
|
||||
class Discrete_conformal_map_parameterizer_3
|
||||
: public Fixed_border_parameterizer_3<ParameterizationMesh_3,
|
||||
|
|
|
|||
|
|
@ -24,7 +24,8 @@
|
|||
|
||||
#include <CGAL/circulator.h>
|
||||
#include <CGAL/Timer.h>
|
||||
#include <CGAL/OpenNL/linear_solver.h>
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
|
||||
#include <CGAL/Parameterizer_traits_3.h>
|
||||
#include <CGAL/Circular_border_parameterizer_3.h>
|
||||
|
|
@ -80,8 +81,8 @@ template
|
|||
class BorderParameterizer_3 ///< Strategy to parameterize the surface border
|
||||
= Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
|
||||
class SparseLinearAlgebraTraits_d ///< Traits class to solve a sparse linear system
|
||||
= OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>
|
||||
>
|
||||
= Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > > >
|
||||
|
||||
class Fixed_border_parameterizer_3
|
||||
: public Parameterizer_traits_3<ParameterizationMesh_3>
|
||||
{
|
||||
|
|
|
|||
|
|
@ -43,15 +43,17 @@ namespace CGAL {
|
|||
|
||||
/// \ingroup PkgSurfaceParameterizationMethods
|
||||
///
|
||||
/// The class LSCM_parameterizer_3 implements the
|
||||
/// The class `LSCM_parameterizer_3` implements the
|
||||
/// *Least Squares Conformal Maps (LSCM)* parameterization \cgalCite{cgal:lprm-lscm-02}.
|
||||
///
|
||||
/// This is a conformal parameterization, i.e. it attempts to preserve angles.
|
||||
///
|
||||
/// This is a free border parameterization. No need to map the surface's border
|
||||
/// This is a free border parameterization. No need to map the border of the surface
|
||||
/// onto a convex polygon (only two pinned vertices are needed to ensure a
|
||||
/// unique solution), but one-to-one mapping is *not* guaranteed.
|
||||
///
|
||||
/// Note that his parametrization method has no template parameter for changing the sparse solver.
|
||||
///
|
||||
/// \cgalModels `ParameterizerTraits_3`
|
||||
///
|
||||
///
|
||||
|
|
@ -66,14 +68,17 @@ template
|
|||
<
|
||||
class ParameterizationMesh_3, ///< 3D surface mesh.
|
||||
class BorderParameterizer_3
|
||||
= Two_vertices_parameterizer_3<ParameterizationMesh_3>,
|
||||
= Two_vertices_parameterizer_3<ParameterizationMesh_3>
|
||||
#ifndef DOXYGEN_RUNNING
|
||||
,
|
||||
///< Strategy to parameterize the surface border.
|
||||
///< The minimum is to parameterize two vertices.
|
||||
class SparseLinearAlgebraTraits_d
|
||||
class SparseLinearAlgebraTraits_d
|
||||
= OpenNL::SymmetricLinearSolverTraits<typename ParameterizationMesh_3::NT>
|
||||
///< Traits class to solve a sparse linear system.
|
||||
///< We may use a symmetric definite positive solver because LSCM
|
||||
///< solves the system in the least squares sense.
|
||||
//< Traits class to solve a sparse linear system.
|
||||
//< We may use a symmetric definite positive solver because LSCM
|
||||
//< solves the system in the least squares sense.
|
||||
#endif
|
||||
>
|
||||
class LSCM_parameterizer_3
|
||||
: public Parameterizer_traits_3<ParameterizationMesh_3>
|
||||
|
|
@ -94,11 +99,11 @@ public:
|
|||
|
||||
/// Export BorderParameterizer_3 template parameter.
|
||||
typedef BorderParameterizer_3 Border_param;
|
||||
/// Export SparseLinearAlgebraTraits_d template parameter.
|
||||
|
||||
// Private types
|
||||
private:
|
||||
typedef SparseLinearAlgebraTraits_d Sparse_LA;
|
||||
|
||||
// Private types
|
||||
private:
|
||||
// Mesh_Adaptor_3 subtypes:
|
||||
typedef typename Adaptor::NT NT;
|
||||
typedef typename Adaptor::Point_2 Point_2;
|
||||
|
|
|
|||
|
|
@ -24,6 +24,7 @@
|
|||
|
||||
#include <CGAL/Fixed_border_parameterizer_3.h>
|
||||
#include <CGAL/surface_mesh_parameterization_assertions.h>
|
||||
#include <CGAL/Eigen_solver_traits.h>
|
||||
|
||||
/// \file Mean_value_coordinates_parameterizer_3.h
|
||||
|
||||
|
|
@ -56,7 +57,7 @@ namespace CGAL {
|
|||
/// \sa `CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
|
||||
/// \sa `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3>`
|
||||
|
||||
template
|
||||
<
|
||||
|
|
@ -64,8 +65,9 @@ template
|
|||
class BorderParameterizer_3 ///< Strategy to parameterize the surface border
|
||||
= Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
|
||||
class SparseLinearAlgebraTraits_d ///< Traits class to solve a sparse linear system
|
||||
= OpenNL::DefaultLinearSolverTraits<typename ParameterizationMesh_3::NT>
|
||||
= Eigen_solver_traits<Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType, Eigen::IncompleteLUT< double > > >
|
||||
>
|
||||
|
||||
class Mean_value_coordinates_parameterizer_3
|
||||
: public Fixed_border_parameterizer_3<ParameterizationMesh_3,
|
||||
BorderParameterizer_3,
|
||||
|
|
|
|||
|
|
@ -407,10 +407,9 @@ int main(int argc, char * argv[])
|
|||
err = CGAL::parameterize(
|
||||
mesh_patch,
|
||||
CGAL::Discrete_authalic_parameterizer_3<
|
||||
Mesh_patch_polyhedron,
|
||||
CGAL::Square_border_arc_length_parameterizer_3<Mesh_patch_polyhedron>,
|
||||
CGAL::Eigen_solver_traits<>
|
||||
>());
|
||||
Mesh_patch_polyhedron,
|
||||
CGAL::Square_border_arc_length_parameterizer_3<Mesh_patch_polyhedron> >()
|
||||
);
|
||||
switch(err) {
|
||||
case Parameterizer::OK: // Success
|
||||
break;
|
||||
|
|
|
|||
|
|
@ -31,7 +31,6 @@ under positional constraints of some of its vertices, without requiring any addi
|
|||
## Concepts ##
|
||||
- `DeformationClosestRotationTraits_3`
|
||||
- `RawPoint_3`
|
||||
- `SparseLinearAlgebraTraitsWithFactor_d`
|
||||
- `SurfaceModelingWeights`
|
||||
|
||||
## Algebraic Traits ##
|
||||
|
|
|
|||
|
|
@ -7,3 +7,5 @@ Stream_support
|
|||
Polyhedron
|
||||
BGL
|
||||
Surface_mesh_parameterization
|
||||
Solver_interface
|
||||
|
||||
|
|
|
|||
|
|
@ -10,7 +10,7 @@
|
|||
\cgalPkgSummaryEnd
|
||||
\cgalPkgShortInfoBegin
|
||||
\cgalPkgSince{3.5}
|
||||
\cgalPkgDependsOn{\ref thirdpartyEigen}
|
||||
\cgalPkgDependsOn{\ref PkgSolverSummary}
|
||||
\cgalPkgBib{cgal:asg-srps}
|
||||
\cgalPkgLicense{\ref licensesGPL "GPL"}
|
||||
\cgalPkgDemo{See Polyhedral Surface,polyhedron_3.zip}
|
||||
|
|
|
|||
|
|
@ -7,3 +7,4 @@ Stream_support
|
|||
Surface_mesher
|
||||
Point_set_processing_3
|
||||
Surface_mesh_parameterization
|
||||
Solver_interface
|
||||
|
|
|
|||
Loading…
Reference in New Issue