CGAL 5.6.3 - Planar Parameterization of Triangulated Surface Meshes

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CGAL::Surface_mesh_parameterization::Square_border_parameterizer_3< TriangleMesh_ > Class Template Referenceabstract
Triangulated Surface Mesh Parameterization Reference » Border Parameterization Methods

`#include <CGAL/Surface_mesh_parameterization/Square_border_parameterizer_3.h>`

Inherited by CGAL::Surface_mesh_parameterization::Square_border_arc_length_parameterizer_3< TriangleMesh_ >, and CGAL::Surface_mesh_parameterization::Square_border_uniform_parameterizer_3< TriangleMesh_ >.

## Definition

template<class TriangleMesh_>
class CGAL::Surface_mesh_parameterization::Square_border_parameterizer_3< TriangleMesh_ >

This is the base class of strategies that parameterize the border of a 3D surface onto a square.

`Square_border_parameterizer_3` is a pure virtual class, thus cannot be instantiated. It implements most of the algorithm. Subclasses only have to implement the function `compute_edge_length()` to compute a segment's length.

The user can provide four vertices on the border of the mesh, which will be mapped to the four corners of the square.

Attention
  The square border parameterizer may create degenerate faces in the parameterization: if an input border vertex has valence `1` and if it is mapped to the same edge of the square as its two adjacent (border) vertices, for example.

Implementation note: To simplify the implementation, the border parameterizer knows only the `TriangleMesh` class and does not know the parameterization algorithm requirements or the kind of sparse linear system used.

Is Model Of:
  `Parameterizer_3`

Template Parameters

  TriangleMesh_ | must be a model of `FaceGraph`.

See also
  `CGAL::Surface_mesh_parameterization::Square_border_uniform_parameterizer_3<TriangleMesh>`
  `CGAL::Surface_mesh_parameterization::Square_border_arc_length_parameterizer_3<TriangleMesh>`

## Public Types
typedef TriangleMesh_ | Triangle_mesh
| Triangle mesh type.
typedef boost::graph_traits< Triangle_mesh >::vertex_descriptor | vertex_descriptor
| Mesh vertex type.
typedef boost::graph_traits< Triangle_mesh >::halfedge_descriptor | halfedge_descriptor
| Mesh halfedge type.

## Public Member Functions
template<typename VertexUVMap , typename VertexIndexMap , typename VertexParameterizedMap >
Error_code | parameterize (const Triangle_mesh &mesh, halfedge_descriptor bhd, VertexUVMap uvmap, VertexIndexMap, VertexParameterizedMap vpmap)
| assigns to the vertices of the border of the mesh a 2D position (i.e. a (u,v) pair) on the border's shape.
bool | is_border_convex () const
| indicates if the border's shape is convex.
| Square_border_parameterizer_3 ()
| Constructor.
| Square_border_parameterizer_3 (vertex_descriptor v0, vertex_descriptor v1, vertex_descriptor v2, vertex_descriptor v3)
| Constructor with user-defined corners: the user provides four vertices of the border of the mesh, which will be parameterized to the corners of the square.

## Constructor & Destructor Documentation

## ◆ Square_border_parameterizer_3()

template<class TriangleMesh_ >

CGAL::Surface_mesh_parameterization::Square_border_parameterizer_3< TriangleMesh_ >::Square_border_parameterizer_3 | ( | vertex_descriptor | v0,
|  | vertex_descriptor | v1,
|  | vertex_descriptor | v2,
|  | vertex_descriptor | v3
| ) |  |

Constructor with user-defined corners: the user provides four vertices of the border of the mesh, which will be parameterized to the corners of the square.

Precondition
  The given vertices must be on the border.

## Member Function Documentation

## ◆ parameterize()

template<class TriangleMesh_ >
template<typename VertexUVMap , typename VertexIndexMap , typename VertexParameterizedMap >

Error_code CGAL::Surface_mesh_parameterization::Square_border_parameterizer_3< TriangleMesh_ >::parameterize | ( | const Triangle_mesh & | mesh,
|  | halfedge_descriptor | bhd,
|  | VertexUVMap | uvmap,
|  | VertexIndexMap | ,
|  | VertexParameterizedMap | vpmap
| ) |  |

assigns to the vertices of the border of the mesh a 2D position (i.e. a (u,v) pair) on the border's shape.

Mark them as parameterized.

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`.
  vpmap | an instantiation of the class `VertexParameterizedMap`.

Precondition
  `mesh` must be a triangular mesh.
  The vertices must be indexed (vimap must be initialized).