#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. More...

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. More...

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.