CGAL::Surface_mesh_parameterization::LSCM_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ > Class Template Reference

#include <CGAL/Surface_mesh_parameterization/LSCM_parameterizer_3.h>

Definition

template<class TriangleMesh_, class BorderParameterizer_ = Default, class SolverTraits_ = Default>
class CGAL::Surface_mesh_parameterization::LSCM_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >

The class LSCM_parameterizer_3 implements the Least Squares Conformal Maps (LSCM) parameterization [8].

This is a conformal parameterization, i.e. it attempts to preserve angles.

This is a free border parameterization. There is 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 a one-to-one mapping is not guaranteed.

Is Model Of:

Parameterizer_3

Template Parameters

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: Two_vertices_parameterizer_3<TriangleMesh_>
SolverTraits_	must be a model of SparseLinearAlgebraTraits_d. Note: We may use a symmetric definite positive solver because LSCM solves the system in the least squares sense. 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: CGAL::Eigen_solver_traits<Eigen::SimplicialLDLT< Eigen::SparseMatrix<double> > > Otherwise, it uses CGAL's wrapping function to the OpenNL library: OpenNL::SymmetricLinearSolverTraits<typename TriangleMesh::NT>

See also

CGAL::Surface_mesh_parameterization::Two_vertices_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>

Public Types
typedef Border_parameterizer_	Border_parameterizer
	The border parameterizer.
typedef SolverTraits_	Solver_traits
	Solver traits type.
typedef TriangleMesh_	Triangle_mesh
	Triangle mesh type.
typedef boost::graph_traits< Triangle_mesh >::halfedge_descriptor	halfedge_descriptor
	Mesh halfedge type.

Public Member Functions
	LSCM_parameterizer_3 (Border_parameterizer border_param=Border_parameterizer(), Solver_traits sparse_la=Solver_traits())
	Constructor.
template<typename VertexUVMap >
bool	is_one_to_one_mapping (const Triangle_mesh &mesh, halfedge_descriptor bhd, const VertexUVMap uvmap) const
	returns whether the 3D -> 2D mapping is one-to-one.
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.

Constructor & Destructor Documentation

LSCM_parameterizer_3()

template<class TriangleMesh_ , class BorderParameterizer_ = Default, class SolverTraits_ = Default>

CGAL::Surface_mesh_parameterization::LSCM_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::LSCM_parameterizer_3	(	Border_parameterizer	border_param = Border_parameterizer(),
		Solver_traits	sparse_la = Solver_traits()
	)

Constructor.

Parameters

border_param	Object that maps the surface's border to 2D space
sparse_la	Traits object to access a sparse linear system

Member Function Documentation

parameterize()

template<class TriangleMesh_ , class BorderParameterizer_ = Default, class SolverTraits_ = Default>

template<typename VertexUVmap , typename VertexIndexMap , typename VertexParameterizedMap >

Error_code CGAL::Surface_mesh_parameterization::LSCM_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::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.

The mapping is piecewise linear (linear in each triangle). The result is the (u,v) pair image of each vertex of the 3D surface.

Template Parameters

VertexUVmap	must be a model of ReadWritePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and Point_2 (type deduced from Triangle_mesh using Kernel_traits) as value type.
VertexIndexMap	must be a model of ReadablePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and a unique integer as value type.
VertexParameterizedMap	must be a model of ReadWritePropertyMap with boost::graph_traits<Triangle_mesh>::vertex_descriptor as key type and a Boolean as value type.

Parameters

mesh	a triangulated surface.
bhd	a halfedge descriptor on the boundary of mesh.
uvmap	an instantiation of the class VertexUVmap.
vimap	an instantiation of the class VertexIndexMap.
vpmap	an instantiation of the class VertexParameterizedMap.

Precondition

mesh must be a triangular mesh.

The vertices must be indexed (vimap must be initialized).