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CGAL 4.5 - Planar Parameterization of Triangulated Surface Meshes
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ParameterizerTraits_3 Concept Reference
Concepts

Definition

ParameterizerTraits_3 is a concept of parameterization object for a given type of mesh, Adaptor, which is a model of the ParameterizationMesh_3 concept.

Design Pattern

ParameterizerTraits_3 models are Strategies [6] : they implement a strategy of surface parameterization for models of ParameterizationMesh_3.

Creation

Construction and destruction are undefined.

Has Models:

CGAL::Parameterizer_traits_3<ParameterizationMesh_3>

CGAL::Fixed_border_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::Barycentric_mapping_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::Discrete_authalic_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::Discrete_conformal_map_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::LSCM_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

CGAL::Mean_value_coordinates_parameterizer_3<ParameterizationMesh_3, BorderParameterizer_3, SparseLinearAlgebraTraits_d>

See Also
ParameterizationMesh_3

Types

typedef unspecified_type Adaptor
 Export the type of mesh to parameterize.
 

Constants

enum  Error_code {
  OK, ERROR_EMPTY_MESH, ERROR_NON_TRIANGULAR_MESH, ERROR_NO_TOPOLOGICAL_DISC,
  ERROR_BORDER_TOO_SHORT, ERROR_NON_CONVEX_BORDER, ERROR_CANNOT_SOLVE_LINEAR_SYSTEM, ERROR_NO_1_TO_1_MAPPING,
  ERROR_OUT_OF_MEMORY, ERROR_WRONG_PARAMETER
}
 List of errors detected by this package. More...
 

Operations

Error_code parameterize (Adaptor &mesh)
 Compute a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space. More...
 

Member Enumeration Documentation

enum ParameterizerTraits_3::Error_code

List of errors detected by this package.

Enumerator
OK 

Success.

ERROR_EMPTY_MESH 

Input mesh is empty.

ERROR_NON_TRIANGULAR_MESH 

Input mesh is not triangular.

ERROR_NO_TOPOLOGICAL_DISC 

Input mesh is not a topological disc.

ERROR_BORDER_TOO_SHORT 

This border parameterization requires a longer border.

ERROR_NON_CONVEX_BORDER 

This parameterization method requires a convex border.

ERROR_CANNOT_SOLVE_LINEAR_SYSTEM 

Cannot solve linear system.

ERROR_NO_1_TO_1_MAPPING 

Parameterization failed: no one-to-one mapping.

ERROR_OUT_OF_MEMORY 

Not enough memory.

ERROR_WRONG_PARAMETER 

A method received an unexpected parameter.

Member Function Documentation

Error_code ParameterizerTraits_3::parameterize ( Adaptor &  mesh)

Compute a one-to-one mapping from a triangular 3D surface mesh to a piece of the 2D space.

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

Precondition
mesh must be a surface with one connected component and no hole. mesh must be a triangular mesh.