CGAL 5.1.2 - Planar Parameterization of Triangulated Surface Meshes
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#include <CGAL/Surface_mesh_parameterization/ARAP_parameterizer_3.h>
The class ARAP_parameterizer_3
implements the Local/Global Approach to Mesh Parameterization [8].
This parameterization allows the user to prioritize angle preservation, shape preservation, or a balance of both. A parameter \(\lambda\) controls whether the priority is given to angle or to shape preservation: when \(\lambda=0\), the parameterization is as-similar-as-possible (ASAP) and is equivalent to the (conforming) LSCM parameterization. As \(\lambda\) grows, the shape preservation becomes more and more important, yielding, when \(\lambda\) goes to infinity, a parameterization that is as-rigid-as-possible (ARAP).
This is a free border parameterization. There is no need to map the border of the surface onto a convex polygon. When \(\lambda=0\), only two pinned vertices are needed to ensure a unique solution. When \(\lambda\) is non-null, the border does not need to be parameterized and a random vertex is pinned.
If flips are present in the initial parameterization, a post-processing step is applied using CGAL::Surface_mesh_parameterization::MVC_post_processor_3<TriangleMesh, SolverTraits_>
to attempt to obtain a valid final embedding.
A one-to-one mapping is not guaranteed.
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 that the system is not symmetric. 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::SparseLU<Eigen_sparse_matrix<double>::EigenType> > Eigen::UmfPackLU<Eigen_sparse_matrix<double>::EigenType> > |
CGAL::Surface_mesh_parameterization::Fixed_border_parameterizer_3<TriangleMesh, BorderParameterizer, SolverTraits>
Public Types | |
typedef Border_parameterizer_ | Border_parameterizer |
typedef SolverTraits_ | Solver_traits |
typedef TriangleMesh_ | TriangleMesh |
Public Member Functions | |
template<typename VertexUVMap > | |
bool | is_one_to_one_mapping (const TriangleMesh &mesh, const Faces_vector &faces, const VertexUVMap uvmap) const |
Check if the 3D -> 2D mapping is one-to-one. | |
template<typename VertexUVMap , typename VertexIndexMap , typename VertexParameterizedMap > | |
Error_code | parameterize (TriangleMesh &mesh, halfedge_descriptor bhd, VertexUVMap uvmap, VertexIndexMap vimap, VertexParameterizedMap vpmap) |
Compute a mapping from a triangular 3D surface mesh to a piece of the 2D space. More... | |
ARAP_parameterizer_3 (NT lambda) | |
Constructor taking only the parameter \(\lambda\). | |
ARAP_parameterizer_3 (Border_parameterizer border_param=Border_parameterizer(), Solver_traits sparse_la=Solver_traits(), NT lambda=1000., unsigned int iterations=50, NT tolerance=1e-6) | |
Default Constructor. More... | |
CGAL::Surface_mesh_parameterization::ARAP_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::ARAP_parameterizer_3 | ( | Border_parameterizer | border_param = Border_parameterizer() , |
Solver_traits | sparse_la = Solver_traits() , |
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NT | lambda = 1000. , |
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unsigned int | iterations = 50 , |
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NT | tolerance = 1e-6 |
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) |
Default Constructor.
border_param | Object that maps the surface's border to the 2D space. |
sparse_la | Traits object to access a sparse linear system. |
lambda | Parameter to give importance to shape or angle preservation. |
iterations | Maximal number of iterations in the energy minimization process. |
tolerance | Minimal energy difference between two iterations for the minimization process to continue. |
Error_code CGAL::Surface_mesh_parameterization::ARAP_parameterizer_3< TriangleMesh_, BorderParameterizer_, SolverTraits_ >::parameterize | ( | TriangleMesh & | mesh, |
halfedge_descriptor | bhd, | ||
VertexUVMap | uvmap, | ||
VertexIndexMap | vimap, | ||
VertexParameterizedMap | vpmap | ||
) |
Compute a 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.
VertexUVmap | must be a model of ReadWritePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and Point_2 (type deduced from TriangleMesh using Kernel_traits ) as value type. |
VertexIndexMap | must be a model of ReadablePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and a unique integer as value type. |
VertexParameterizedMap | must be a model of ReadWritePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key type and a Boolean as value type. |
mesh | a triangulated surface. |
bhd | a halfedge descriptor on the boundary of mesh . |
uvmap | an instanciation of the class VertexUVmap . |
vimap | an instanciation of the class VertexIndexMap . |
vpmap | an instanciation of the class VertexParameterizedMap . |
mesh
must be a triangular mesh.