The general definition of input meshes handled directly by CGAL::parameterize() is:

Model of ParameterizationMesh_3.
Triangulated.
2-manifold.
Oriented.
Homeomorphic to a disc (may have holes).

This package provides a model of the ParameterizationMesh_3 concept to access CGAL::Polyhedron_3<Traits>:

CGAL::Parameterization_polyhedron_adaptor_3<Polyhedron_3_>

The meshes supported indirectly by the package can be of any genus and have any number of connected components. If it is not a topological disc, the input mesh has to come with a description of a cutting path (an oriented list of vertices) which is the border of a topological disc. If no cutting path is given as input, we assume that the surface border is the longest border already in the input mesh (the other borders will be considered as holes).

The CGAL::Parameterization_mesh_patch_3<ParameterizationPatchableMesh_3> class is responsible for virtually cutting a patch in a ParameterizationPatchableMesh_3 mesh. The resulting patch is a topological disk (if the input cutting path is correct) and provides a ParameterizationMesh_3 interface. It can be used as parameter of CGAL::parameterize().

Note that this way the user is responsible for cutting a closed mesh of arbitrary genus (even a topological disc with an intricate seam cut), as long as this condition is fulfilled.

The package provides an interface with CGAL::Polyhedron_3<Traits>:

CGAL::Parameterization_polyhedron_adaptor_3<Polyhedron_3_>

Classes
class	CGAL::Parameterization_polyhedron_adaptor_3< Polyhedron_3_ >
	`Parameterization_polyhedron_adaptor_3` is an adaptor class to access to a Polyhedron 3D mesh using the `ParameterizationPatchableMesh_3` interface. More...

class	CGAL::Parameterization_mesh_patch_3< ParameterizationPatchableMesh_3 >
	Parameterization_mesh_patch_3 is a Decorator class to virtually cut a patch in a ParameterizationPatchableMesh_3 3D surface. More...

Classes