mirror of https://github.com/CGAL/cgal
Do not explain OpenNL and say that LSCM has no parameter for a solver
This commit is contained in:
Andreas Fabri
parent
06a102731b
commit
8ae42933c7
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@ -17,25 +17,6 @@ The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be available o
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\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
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\sa `CGAL::Eigen_vector<T>`
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Example
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--------------
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The instantiation of this class assumes an \ref thirdpartyEigen "Eigen" sparse solver is provided. Here are few examples:
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\code{.cpp}
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typedef CGAL::Eigen_sparse_matrix<double>::EigenType EigenMatrix;
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//iterative general solver
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typedef CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<EigenMatrix> > Iterative_general_solver;
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//iterative symmetric solver
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typedef CGAL::Eigen_solver_traits< Eigen::ConjugateGradient<EigenMatrix> > Iterative_symmetric_solver;
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//direct symmetric solver
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typedef CGAL::Eigen_solver_traits< Eigen::SimplicialCholesky<EigenMatrix> > Direct_symmetric_solver;
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\endcode
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*/
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template< typename T >
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@ -31,16 +31,16 @@ SparseLinearAlgebraTraitsWithFactor_d();
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/// @{
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/*!
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Factorize the sparse matrix A.
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This factorization is used in SparseLinearAlgebraTraitsWithFactor_d::linear_solver to solve the system for different right-hand side vectors.
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Factorize the sparse matrix `A`.
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This factorization is used in `SparseLinearAlgebraTraitsWithFactor_d::linear_solver()` to solve the system for different right-hand side vectors.
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See `::SparseLinearAlgebraTraits_d::linear_solver()` for the description of `D`.
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@return true if the factorization is successful
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@return `true` if the factorization is successful
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*/
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bool factor(const Matrix& A, NT& D);
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/*!
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Solve the sparse linear system \f$ A \times X = B\f$, with \f$ A \f$ being the matrix provided in SparseLinearAlgebraTraitsWithFactor_d::factor.
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@return true if the solver is successful
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Solve the sparse linear system \f$ A \times X = B\f$, with \f$ A \f$ being the matrix provided in `SparseLinearAlgebraTraitsWithFactor_d::factor()`.
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@return `true` if the solver is successful
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*/
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bool linear_solver(const Vector& B, Vector& X);
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@ -8,8 +8,6 @@ The concept `SparseLinearAlgebraTraits_d` is used to solve sparse linear systems
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\cgalHasModel `CGAL::Eigen_solver_traits<T>`
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\cgalHasModel `OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
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\cgalHasModel `OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
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*/
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@ -73,7 +71,6 @@ bool linear_solver(const Matrix& A, const Vector& B, Vector& X, NT& D);
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`SparseLinearAlgebraTraits_d::Vector` is a concept of a vector that can be multiplied by a sparse matrix.
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\cgalHasModel `CGAL::Eigen_vector<T>`
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\cgalHasModel `OpenNL::FullVector<T>` in the `OpenNL` package
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\sa `SparseLinearAlgebraTraits_d`
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\sa `SparseLinearAlgebraTraits_d::Matrix`
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@ -148,7 +145,6 @@ NT& operator[](int row);
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\cgalHasModel `CGAL::Eigen_sparse_matrix<T>`
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\cgalHasModel `CGAL::Eigen_sparse_symmetric_matrix<T>`
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\cgalHasModel `OpenNL::SparseMatrix<T>` in `OpenNL` package
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\sa `SparseLinearAlgebraTraits_d`
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\sa `SparseLinearAlgebraTraits_d::Vector`
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@ -15,12 +15,31 @@ all use the \ref thirdpartyEigen library.
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\section SectionSolverConcepts Solver Concepts
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\section SectionSolverEigen Eigen
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An interface to all sparse solvers from the \ref thirdpartyEigen
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library is provided through the class
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`Eigen_solver_traits<T>`. This solver traits class can be used for an
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iterative or a direct, symmetric or general sparse solvers. The
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specific solver to be used must be given as template
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parameter.
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Here are few examples:
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\code{.cpp}
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typedef CGAL::Eigen_sparse_matrix<double>::EigenType EigenMatrix;
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//iterative general solver
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typedef CGAL::Eigen_solver_traits< Eigen::BiCGSTAB<EigenMatrix> > Iterative_general_solver;
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//iterative symmetric solver
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typedef CGAL::Eigen_solver_traits< Eigen::ConjugateGradient<EigenMatrix> > Iterative_symmetric_solver;
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//direct symmetric solver
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typedef CGAL::Eigen_solver_traits< Eigen::SimplicialCholesky<EigenMatrix> > Direct_symmetric_solver;
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\endcode
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@ -79,6 +79,7 @@ class Eigen_solver_traits
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typedef typename EigenSolverT::Scalar Scalar;
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// Public types
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public:
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typedef EigenSolverT Solver;
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typedef Scalar NT;
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typedef typename internal::Get_eigen_matrix<EigenSolverT,NT>::type Matrix;
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typedef Eigen_vector<Scalar> Vector;
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@ -143,6 +144,7 @@ class Eigen_solver_traits< Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenTyp
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typedef EigenSolverT::Scalar Scalar;
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// Public types
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public:
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typedef EigenSolverT Solver;
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typedef Scalar NT;
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typedef internal::Get_eigen_matrix<EigenSolverT,NT>::type Matrix;
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typedef Eigen_vector<Scalar> Vector;
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@ -54,7 +54,7 @@ This \cgal package implements several parameterization methods:
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- `CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
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- `CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
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- `CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
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- `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
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- `CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3>`
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- `CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`
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## Border Parameterization Methods ##
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@ -121,16 +121,6 @@ The package provides an interface with `CGAL::Polyhedron_3<Traits>`:
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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.
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## Sparse Linear Algebra ##
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Since parameterizing meshes requires
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efficient representation of sparse matrices and efficient iterative or
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direct linear solvers, we provide an interface to several
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sparse linear solvers:
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- <span class="textsc">Eigen</span> 3.1 (or greater) is the library recommended by %CGAL solving sparse systems.
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- OpenNL (authored by Bruno Lévy) is shipped with %CGAL is the default solver.
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- `OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
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- `OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
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## Helper Classes ##
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@ -249,18 +239,6 @@ The package provides an interface with `CGAL::Polyhedron_3<Traits>`:
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/*! \defgroup PkgSurfaceParameterizationAlgebra Sparse Linear Algebra
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\ingroup PkgSurfaceParameterization
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Since parameterizing meshes requires
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efficient representation of sparse matrices and efficient iterative or
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direct linear solvers, we provide an interface to several
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sparse linear solvers:
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- <span class="textsc">Eigen</span> 3.1 (or greater) is the library recommended by %CGAL solving sparse systems.
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- OpenNL (authored by Bruno Lévy) is shipped with %CGAL is the default solver.
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- `OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
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- `OpenNL::SymmetricLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` in OpenNL package
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*/
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/*!
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\defgroup PkgSurfaceParameterizationHelper Helper Class
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@ -40,9 +40,8 @@ data structure.
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Since parameterizing meshes require efficient representation of sparse
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matrices and efficient iterative or direct linear solvers, we provide
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a unified interface to a linear solver library (\ref thirdpartyEigen "Eigen"),
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and propose a separate package devoted to OpenNL sparse
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linear solver.
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a unified interface to linear solvers as described in Chapter
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\ref PkgSolverSummary.
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Note that linear solvers commonly use double precision floating point
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numbers. Therefore, this package is intended to be used with a \cgal %Cartesian kernel with doubles.
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@ -69,8 +68,8 @@ Parameterizer_traits_3<ParameterizationMesh_3>::Error_code parameterize (Paramet
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The function `parameterize()` applies a default surface parameterization
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method, namely Floater Mean Value Coordinates \cgalCite{cgal:f-mvc-03}, with an
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arc-length circular border parameterization, and using OpenNL sparse
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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.
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arc-length circular border parameterization, and using a sparse
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linear solver from the \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.
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The mesh must be a triangle mesh surface with one connected component.
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Note: `Parameterizer_traits_3<ParameterizationMesh_3>` is the (pure virtual) superclass of all surface parameterizations and defines the error codes.
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@ -155,7 +154,7 @@ and \ref secBorderParameterizationsforFreeMethods.
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\subsection Surface_mesh_parameterizationTheSparseLinearAlgebraTraitsd The SparseLinearAlgebraTraits_d Concept
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This package solves sparse linear systems using solvers which are models
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of `SparseLinearAlgebraTraits_d`. See Section \ref secSparseLinearAlgebra.
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of `SparseLinearAlgebraTraits_d`. See Chapter \ref PkgSolverSummary.
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\subsection Surface_mesh_parameterizationTheParameterizationMesh3 The ParameterizationMesh_3 and ParameterizationPatchableMesh_3 Concepts
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@ -419,65 +418,7 @@ Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer()
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\endcode
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\section secSparseLinearAlgebra Sparse Linear Algebra
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Parameterizing triangle meshes requires both efficient representation
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of sparse matrices and efficient iterative or direct linear
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solvers. We provide links to \ref thirdpartyEigen "Eigen" library
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and include a separate package devoted to OpenNL sparse linear solver.
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\subsection Surface_mesh_parameterizationListofSolvers List of Solvers
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We provide an interface to several sparse linear solvers, as models
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of the `SparseLinearAlgebraTraits_d` concept:
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- An interface to sparse solvers from the `OpenNL` library \cgalCite{cgal:l-nmdgp-05} is provided through classes
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`OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` and
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`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
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supports exact number types.
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- An interface to all sparse solvers from the \ref thirdpartyEigen "Eigen" library is provided through the class
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`Eigen_solver_traits<T>`. This solver traits class can be used for an iterative or a direct,
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symmetric or general sparse solvers. The \ref thirdpartyEigen "Eigen" solver to be used must be given as template parameter.
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\subsection Surface_mesh_parameterizationEigenSolver Eigen Solver Example
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The example \ref Surface_mesh_parameterization/Eigen_parameterization.cpp "Eigen_parameterization.cpp" computes the
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default parameterization method (Floater mean value coordinates with a circular border),
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but specifically instantiates an \ref thirdpartyEigen "Eigen" solver. Specifying a specific solver
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instead of the default one (OpenNL) means using the third parameter of
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`Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>`. The differences with the first
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example \ref Surface_mesh_parameterization/Simple_parameterization.cpp "Simple_parameterization.cpp" are:
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\code{.cpp}
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#include <CGAL/Eigen_solver_traits.h>
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...
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//***************************************
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// Floater Mean Value Coordinates parameterization
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// (circular border) with Eigen solver
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//***************************************
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// Circular border parameterizer (the default)
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typedef CGAL::Circular_border_arc_length_parameterizer_3<Parameterization_polyhedron_adaptor>
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Border_parameterizer;
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// Eigen solver
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typedef CGAL::Eigen_solver_traits<> Solver;
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// Floater Mean Value Coordinates parameterization
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// (circular border) with Eigen solver
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typedef CGAL::Mean_value_coordinates_parameterizer_3<Parameterization_polyhedron_adaptor,
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Border_parameterizer,
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Solver>
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Parameterizer;
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Parameterizer::Error_code err = CGAL::parameterize(mesh_adaptor, Parameterizer());
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...
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\endcode
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\section secCuttingaMesh Cutting a Mesh
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@ -605,63 +546,7 @@ and is therefore non-singular (Gram theorem).
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</UL>
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\subsection Surface_mesh_parameterizationPrecision Precision
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Two algorithms of this package construct the sparse linear system(s)
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using trigonometric functions, and are this incompatible with exact arithmetic:
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<UL>
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<LI>Floater mean value coordinates
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<LI>Circular border parameterization
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</UL>
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On the other hand, linear solvers commonly use double precision floating point
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numbers.
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OpenNL's BICGSTAB solver (accessible through the
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`OpenNL::DefaultLinearSolverTraits<COEFFTYPE, MATRIX, VECTOR, SOLVER>` interface)
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is the only solver supported by this package which
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computes exact results, when used with an exact arithmetic. This package is
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intended to be used mainly with a \cgal %Cartesian kernel with doubles.
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\subsection Surface_mesh_parameterizationOpenNLsBICGSTAB OpenNL's BICGSTAB Solver with an Exact Arithmetic
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The BICGSTAB conjugate gradient is in disguise a direct solver.
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In a nutshell, it computes a vector basis
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orthogonal with respect to the matrix, and the coordinates of the solution in this vector basis.
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Each iteration computes one component of the basis and one coordinate, therefore the algorithm
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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.
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\subsection Surface_mesh_parameterizationSolverswith Solvers with a Floating Point Arithmetic
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<I>OpenNL's BICGSTAB example:</I>
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When inexact numerical types are used (e.g. doubles), accumulated errors slow down convergence
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(in practice, it requires approximately \f$ 5k\f$ iterations to converge).
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The required number of iterations depends on the eigenvalues of the matrix, and these eigenvalues depend
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on the shape of the triangles. The optimum is when the triangles are equilateral (then the solver converges
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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
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is wide (many different eigenvalues), and the solver requires nearly \f$ 5n\f$ iterations to converge.
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\subsection Surface_mesh_parameterizationAlgorithmic Algorithmic Complexity
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In this package, we focus on piecewise linear mappings onto a planar
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domain. All surface parameterization methods are based on solving one (or two)
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sparse linear system(s).
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The algorithmic complexity is dominated by the resolution of the sparse linear system(s).
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<I>OpenNL's BICGSTAB example:</I>
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At each iteration, the operation of highest complexity is the product between the sparse-matrix and a vector.
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The sparse matrix has a fixed number of non-zero coefficients per row,
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therefore the matrix / vector product has \f$ O(n)\f$ complexity.
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Since convergence is reached after \f$ k\f$ iterations, the complexity is \f$ O(k.n)\f$
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(where \f$ k\f$ is the number of distinct eigenvalues of the matrix).
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Therefore, best case complexity is \f$ O(n)\f$ (equilateral triangles),
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and worst case complexity is \f$ O(n^2)\f$ (skinny triangles).
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\section Surface_mesh_parameterizationSoftware Software Design
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@ -801,7 +686,7 @@ The purpose of such a model is to:
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<LI>Support several kind of meshes.
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<LI>Hide the implementation of extra fields specific to the parameterization domain
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(`index`, `u`, `v`, `is_parameterized`).
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<LI>Handle in the mesh type the complexity of <I>virtually</I> cutting a mesh
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<LI>%Handle in the mesh type the complexity of <I>virtually</I> cutting a mesh
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to make it homeomorphic to a disk (instead of duplicating this
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code in each parameterization method).
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</OL>
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@ -834,15 +719,6 @@ This mainly means that:
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can be set <I>per corner</I> (which is a more general way of saying <I>per half-edge</I>).
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</UL>
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\subsection Surface_mesh_parameterizationSparseLinearAlgebraTraitsd SparseLinearAlgebraTraits_d Concept
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This package solves sparse linear systems using solvers which are models
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of `SparseLinearAlgebraTraits_d`.
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`SparseLinearAlgebraTraits_d` is a sub-concept of the `LinearAlgebraTraits_d` concept
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in `Kernel_d`.
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The goal is to adapt easily code written for dense matrices to sparse ones,
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and vice-versa.
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\subsection Surface_mesh_parameterizationCuttingaMesh_1 Cutting a Mesh
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@ -855,23 +731,7 @@ not intend to cover this topic at the moment.
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\section Surface_mesh_parameterizationExtendingthe Extending the Package and Reusing Code
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\subsection Surface_mesh_parameterizationReusingMesh Reusing Mesh Adaptors
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`ParameterizationMesh_3` defines a concept to access to a
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general polyhedral mesh.
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It is optimized for the `Surface_mesh_parameterization` package
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only in the sense that it
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defines the accessors to fields specific to the parameterization domain
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(`index`, `u`, `v`, `is_parameterized`).
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It may be easily generalized.
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\subsection Surface_mesh_parameterizationReusingSparse Reusing Sparse Linear Algebra
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The `SparseLinearAlgebraTraits_d` concept and the traits classes
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for \ref thirdpartyEigen "Eigen" and OpenNL are independent of the rest of the
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`Surface_mesh_parameterization` package, and may be reused by
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\cgal developers for other purposes.
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\subsection Surface_mesh_parameterizationAddingNewParameterization Adding New Parameterization Methods
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@ -7,3 +7,4 @@ Stream_support
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Polyhedron
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Kernel_d
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Solver_interface
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Convex_hull_2
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@ -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>
|
||||
|
|
|
|||
|
|
@ -66,25 +66,26 @@ 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) {
|
||||
|
|
|
|||
|
|
@ -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,
|
||||
|
|
|
|||
Loading…
Reference in New Issue