CGAL 6.0.1 - Planar Parameterization of Triangulated Surface Meshes
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#include <CGAL/Surface_mesh_parameterization/Discrete_conformal_map_parameterizer_3.h>
The class Discrete_conformal_map_parameterizer_3
implements the Discrete Conformal Map (DCM) parameterization.
This algorithm is also called Discrete Conformal Parameterization (DCP), Discrete Harmonic Map or Fixed Conformal Parameterization by other authors [3].
This is a conformal parameterization, i.e. it attempts to preserve angles.
A one-to-one mapping is guaranteed if the surface's border is mapped onto a convex polygon.
This class is a strategy called by the main parameterization algorithm Fixed_border_parameterizer_3::parameterize()
and it:
BorderParameterizer_
and SolverTraits_
.compute_w_ij()
to compute w_ij
, the (i,j)
-coefficient of matrix A
, for j
neighbor vertex of i
, based on Discrete Conformal Map method.Parameterizer_3
TriangleMesh_ | must be a model of FaceGraph |
BorderParameterizer_ | is a strategy to parameterize the surface border and must be a model of Parameterizer_3 .Default: This class parameterizes the border of a 3D surface onto a circle, with an arc-length parameterizatio... Definition: Circular_border_parameterizer_3.h:244 |
SolverTraits_ | must be a model of SparseLinearAlgebraTraits_d .Note that the system is not symmetric because Fixed_border_parameterizer_3 does not remove border vertices from the system.Default: If Eigen 3.1 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, then an overload of Eigen_solver_traits is provided as default parameter: Eigen::BiCGSTAB<Eigen_sparse_matrix<double>::EigenType,
Eigen::IncompleteLUT< double > > >
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CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>
Public Types | |
typedef Border_parameterizer_ | Border_parameterizer |
Border parameterizer type. | |
typedef SolverTraits_ | Solver_traits |
Solver traits type. | |
typedef TriangleMesh_ | Triangle_mesh |
Triangle mesh type. | |
Public Types inherited from CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ > | |
typedef Border_parameterizer_ | Border_parameterizer |
Border parameterizer type. | |
typedef SolverTraits_ | Solver_traits |
Solver traits type. | |
typedef TriangleMesh_ | Triangle_mesh |
Triangle mesh type. | |
typedef boost::graph_traits< Triangle_mesh >::vertex_descriptor | vertex_descriptor |
Mesh vertex type. | |
typedef boost::graph_traits< Triangle_mesh >::halfedge_descriptor | halfedge_descriptor |
Mesh halfedge type. | |
typedef Solver_traits::Vector | Vector |
Solver vector type. | |
typedef Solver_traits::Matrix | Matrix |
Solver matrix type. | |
Public Member Functions | |
Discrete_conformal_map_parameterizer_3 (Border_parameterizer border_param=Border_parameterizer(), Solver_traits sparse_la=Solver_traits()) | |
Constructor. | |
Public Member Functions inherited from CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ > | |
Fixed_border_parameterizer_3 (Border_parameterizer border_param=Border_parameterizer(), Solver_traits sparse_la=Solver_traits()) | |
Constructor. | |
virtual | ~Fixed_border_parameterizer_3 () |
Destructor of base class should be virtual. | |
template<typename VertexUVmap , typename VertexIndexMap , typename VertexParameterizedMap > | |
Error_code | parameterize (Triangle_mesh &mesh, halfedge_descriptor bhd, VertexUVmap uvmap, VertexIndexMap vimap, VertexParameterizedMap vpmap) |
computes a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space. | |
Protected Member Functions | |
virtual NT | compute_w_ij (const Triangle_mesh &mesh, vertex_descriptor main_vertex_v_i, Vertex_around_target_circulator< Triangle_mesh > neighbor_vertex_v_j) const |
computes w_ij , the (i,j) -coefficient of matrix A , for j neighbor vertex of i . | |
Protected Member Functions inherited from CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ > | |
template<typename VertexUVmap , typename VertexIndexMap > | |
void | initialize_system_from_mesh_border (Matrix &A, Vector &Bu, Vector &Bv, const Triangle_mesh &mesh, halfedge_descriptor bhd, VertexUVmap uvmap, VertexIndexMap vimap) const |
initializes A , Bu and Bv after border parameterization. | |
virtual NT | compute_w_ij (const Triangle_mesh &mesh, vertex_descriptor main_vertex_v_i, Vertex_around_target_circulator< Triangle_mesh > neighbor_vertex_v_j) const =0 |
computes w_ij , coefficient of matrix A for j neighbor vertex of i . | |
template<typename VertexIndexMap > | |
Error_code | setup_inner_vertex_relations (Matrix &A, Vector &, Vector &, const Triangle_mesh &mesh, vertex_descriptor vertex, VertexIndexMap vimap) const |
Compute the line i of matrix A for i inner vertex: | |
Border_parameterizer & | get_border_parameterizer () |
Get the object that maps the surface's border onto a 2D space. | |
Solver_traits & | get_linear_algebra_traits () |
Get the sparse linear algebra (traits object to access the linear system). | |
CGAL::Surface_mesh_parameterization::Discrete_conformal_map_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::Discrete_conformal_map_parameterizer_3 | ( | Border_parameterizer | border_param = Border_parameterizer() , |
Solver_traits | sparse_la = Solver_traits() |
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) |
Constructor.
border_param | Object that maps the surface's border to 2D space. |
sparse_la | Traits object to access a sparse linear system. |
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protectedvirtual |
computes w_ij
, the (i,j)
-coefficient of matrix A
, for j
neighbor vertex of i
.
mesh | a triangulated surface. |
main_vertex_v_i | the vertex of mesh with index i |
neighbor_vertex_v_j | the vertex of mesh with index j |