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Sébastien Loriot 2014-10-17 14:23:24 +02:00
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\chapter{Advancing Front Surface Reconstuction}
\label{chap:surface_reconstruction}
\ccChapterAuthor{Frank Da and David Cohen-Steiner}
\section{Introduction}
This package offers an algorithm for surface reconstruction from an unorganized point set.
The algorithm selects facets of the 3D Delaunay triangulation of the points.

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\begin{ccRefClass}{AFSR_cell_base_3<Kernel, CellBase >}
\ccDefinition
The class \ccRefName\ is the cell class that must be blended in the cell parameter
of the 3D Delaunay triagulation. It mainly provides storage and methods used by the
Advancing front surface reconstruction algorithm.
\ccInclude{CGAL/AFSR_cell_base_3.h}
\ccInheritsFrom
\ccc{CellBase}
%\ccTypes
%\ccTypedef{typedef Kernel::FT FT;}{The number type.}
%\ccCreation
%\ccCreationVariable{c}
%\ccConstructor{AFSR_cell_base_3();}{Default constructor}
%\ccOperations
%\ccMemberFunction{bool has_facet_on_surface(int i) const;}{Returns \ccc{true}, iff the facet is on the surface.}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\begin{ccRefClass}{AFSR_options}
\ccDefinition
The class \ccRefName\ is used as a container of the options of the surface reconstruction algorithm.
\ccInclude{CGAL/AFSR_options.h}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\begin{ccRefClass}{AFSR_vertex_base_3<Kernel,VertexBase>}
\ccDefinition
The class \ccRefName\ is the vertex class that must be blended in the vertex parameter
of the 3D Delaunay triagulation. It mainly provides storage and methods used by the
Advancing front surface reconstruction algorithm.
\ccInclude{CGAL/AFSR_vertex_base_3.h}
\ccInheritsFrom
\ccc{VertexBase}
%\ccTypes
%\ccTypedef{typedef Kernel::FT FT;}{The number type.}
%\ccCreation
%\ccCreationVariable{v}
%\ccConstructor{Surface_vertex_base_2();}{Default constructor}
%\ccOperations
%\ccMemberFunction{Vertex_handle_3 vertex_3() const;}{Returns the vertex handle in the 3D Delaunay triangulation.}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\begin{ccRefClass}{AFSR_vertex_base_with_id_3<Kernel, VertexBase >}
\ccDefinition
The class \ccRefName\ is the vertex class that must be blended in the vertex parameter
of the 3D Delaunay triagulation. It mainly provides storage and methods used by the
Advancing front surface reconstruction algorithm.
\ccInclude{CGAL/AFSR_vertex_base_with_id_3.h}
%\ccTypes
%\ccTypedef{typedef Kernel::FT FT;}{The number type.}
%\ccCreation
\ccCreationVariable{v}
%\ccConstructor{Surface_vertex_base_2();}{Default constructor}
\ccOperations
\ccMemberFunction{int& id() const;}{Returns a reference to an \ccc{int} that is not used or altered by the
surface reconstruction algorithm.}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\begin{ccRefClass}{Advancing_front_surface_reconstruction<Kernel,Delaunay_3>}
\ccDefinition
The class \ccRefName\ extracts a surface from a 3D Delaunay triangulation.
\ccInclude{CGAL/Advancing_front_surface_reconstruction.h}
\ccParameters
The parameter for \ccc{Delaunay_3} must be a 3D Delaunay triangulation where \ccc{CGAL::AFSR_vertex_base_3}
or \ccc{CGAL::AFSR_vertex_base_with_id_3} and \ccc{CGAL::AFSR_cell_base_3} must be blended in the vertex and face class.
\ccTypes
\ccTypedef{typedef Delaunay_3 Triangulation_3;}{}
\ccTypedef{typedef CGAL::Triple<Cell_handle, int,int> Edge;}{For \ccc{(ch,i,j)}, this is the edge between vertices \ccc{i} and \ccc{j} in cell \ccc{*ch}.}
\ccTypedef{typedef std::pair<Edge,int> Edge_incident_facet;}{For \ccc{((ch,i,j),k)}, this is the facet adjacent to the edge \ccc{(,i,j)}, and
opposite to vertex \ccc{k}, in the cell \ccc{*ch}.}
\ccGlue
\ccNestedType{TDS_2}{The type of the 2D triangulation data structure describing the reconstructed surface.}
\ccNestedType{TDS_2::Vertex}{It is model of the concept \ccc{TriangulationDataStructure_2::Vertex} and has additionally the
method \ccc{vertex_3()} that returns a \ccc{Triangulation_3::Vertex_handle} to the associated 3D vertex.}
\ccNestedType{TDS_2::Face}{It is model of the concept \ccc{TriangulationDataStructure_2::Face} and has additionally the
method \ccc{facet()} that returns the associated \ccc{Triangulation_3::Facet}.}
\ccNestedType{Boundary_iterator}{This forward iterator allows to visit all contours. It
visits the entry point of the contour twice. This allows to
detect that the traversal of the border is finished. One more increment
brings us to the vertex on the next boundary. The value type of the iterator is \ccc{Triangulation_3::Vertex_handle}.}
\ccNestedType{Outlier_iterator}{This bidirectional iterator allows to enumerate all points that were removed
from the 3D Delaunay triangulation during the surface reconstruction. The value type
of the iterator is \ccc{Kernel::Point_3}.}
\ccCreation
\ccCreationVariable{es}
\ccConstructor{Advancing_front_surface_reconstruction(Delaunay_3& del, AFSR_options opt);}{}
\ccOperations
\ccMemberFunction{const TDS_2& tds_2() const;}{Returns a const reference to the reconstructed surface. }
\ccMemberFunction{bool is_on_surface(TDS_2::Vertex_handle vh;}{Returns true, iff the vertex is on the reconstructed surface.}
\ccMemberFunction{const Triangulation_3& triangulation() const;}{Returns a const reference to the 3D Delaunay triangulation.}
\ccMemberFunction{Boundary_iterator boundaries_begin() const;}{}
\ccMemberFunction{Boundary_iterator boundaries_end() const;}{}
\ccMemberFunction{Outlier_iterator outliers_begin() const;}{}
\ccMemberFunction{Outlier_iterator outliers_end() const;}{}
\ccMemberFunction{bool has_on_surface(Triangulation_3::Facet f) const;}
{Returns \ccc{true}, iff the facet is on the reconstructed surface.}
\ccMemberFunction{Edge_incident_facet next(const Edge_incident_facet& f) const;}{returns the next facet around the edge.}
\ccMemberFunction{Edge_incident_facet previous(const Edge_incident_facet& f) const;}{returns the previous facet around the edge.}
\ccMemberFunction{Facet next_surface_facet(const Edge_incident_facet& f) const}{returns the next facet ariund the edge,
which is on the reconstructed surface.}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\begin{ccRefClass}{AFSR::Surface_face_base_2<Kernel, Facet, Fb_2 >}
\ccDefinition
The class \ccRefName\ is the face class used in the triangulation data structure
that describes the reconstructed surface. A face is either part of this
surface, or it is not part of the surface but adjacent to the boundary of the surface.
The face class stores a facet of the 3D Delaunay triangulation, if it
is part of the surface.
\ccInclude{CGAL/AFSR/Surface_face_base_2.h}
%\ccTypes
%\ccTypedef{typedef Kernel::FT FT;}{The number type.}
%\ccCreation
\ccCreationVariable{f}
%\ccConstructor{Surface_face_base_2();}{Default constructor}
\ccOperations
\ccMemberFunction{Facet facet() const;}{Returns the facet in the 3D Delaunay triangulation.}
\ccMemberFunction{bool is_on_surface() const;}{Returns \ccc{true}, iff the face is on the surface.}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\begin{ccRefClass}{AFSR::Surface_vertex_base_2<Kernel, Vh_3, Vb_2 >}
\ccDefinition
The class \ccRefName\ is the vertex class used in the 2D triangulation data structure
that describes the reconstructed surface. It stores a vertex handle to its
correpsonding vertex in the 3D Delaunay triangulation.
\ccInclude{CGAL/AFSR/Surface_vertex_base_2.h}
%\ccTypes
%\ccTypedef{typedef Kernel::FT FT;}{The number type.}
%\ccCreation
\ccCreationVariable{v}
%\ccConstructor{Surface_vertex_base_2();}{Default constructor}
\ccOperations
\ccMemberFunction{Vertex_handle_3 vertex_3() const;}{Returns the vertex handle in the 3D Delaunay triangulation.}
%\ccSeeAlso
%\ccRefIdfierPage{}
\end{ccRefClass}

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\chapter{Advancing Front Surface Reconstruction}
\label{chap:surface_reconstruction_ref}
\ccChapterAuthor{Frank Da and David Cohen-Steiner}
\ccHeading{Classes}
\ccRefIdfierPage{CGAL::Advancing_front_surface_reconstruction}\\
\ccRefIdfierPage{CGAL::AFSR_options}\\
\ccRefIdfierPage{CGAL::AFSR_face_base_3}\\
\ccRefIdfierPage{CGAL::AFSR_vertex_base_3}\\
\ccRefIdfierPage{CGAL::AFSR_vertex_base_with_id_3}
\ccHeading{Functions}
\ccRefIdfierPage{CGAL::write_to_file_vrml2}

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\input{Advancing_front_surface_reconstruction_ref/intro.tex}
\input{Advancing_front_surface_reconstruction_ref/Advancing_front_surface_reconstruction.tex}
\input{Advancing_front_surface_reconstruction_ref/AFSR_cell_base_3.tex}
\input{Advancing_front_surface_reconstruction_ref/AFSR_vertex_base_3.tex}
\input{Advancing_front_surface_reconstruction_ref/AFSR_vertex_base_with_id_3.tex}
\input{Advancing_front_surface_reconstruction_ref/write_to_file_vrml2.tex}

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\begin{ccRefFunction}{write_to_file_vrml2}
\ccDefinition
The function \ccRefName\ writes the reconstructed surface to a file.
\ccInclude{CGAL/IO/Advancing_front_surface_reconstruction.h}
\ccFunction{template <class Surface>
void
write_to_file_vrml2(char* foutput, const Surface& S,
bool boundary, double red, double green, double blue, bool no_header);}
{Opens a file with the basename \ccc{foutput} and the file extension \ccc{.wrl}, and writes the
reconstructed surface to this file. If \ccc{boundary} is \ccc{true} the boundary is drawn.
The color of the facets is defined by \ccc{red}, \ccc{green}, and \ccc{blue}. If \ccc{no_header} is
\ccc{true}, the VRML header is not written.}
\end{ccRefFunction}