\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Planar Parameterization of Triangulated Surface Meshes

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BorderParameterizer_3 Concept Reference
Concepts

## Definition

`BorderParameterizer_3` is a concept of class that parameterizes a given type of mesh, `Adaptor`, which is a model of the `ParameterizationMesh_3` concept.

Implementation note: To simplify the implementation, `BorderParameterizer_3` models know only the `ParameterizationMesh_3` class. They do not know the parameterization algorithm requirements or the kind of sparse linear system used.

## Design Pattern

`BorderParameterizer_3` models are Strategies [6] : they implement a strategy of border parameterization for models of `ParameterizationMesh_3`.

## Creation

Construction and destruction are undefined.

Has Models:

  `CGAL::Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>`

  `CGAL::Circular_border_uniform_parameterizer_3<ParameterizationMesh_3>`

  `CGAL::Square_border_arc_length_parameterizer_3<ParameterizationMesh_3>`

  `CGAL::Square_border_uniform_parameterizer_3<ParameterizationMesh_3>`

  `CGAL::Two_vertices_parameterizer_3<ParameterizationMesh_3>`

See Also
  `ParameterizerTraits_3`
  `ParameterizationMesh_3`

## Types
typedef unspecified_type | Adaptor
| Export `ParameterizationMesh_3` template parameter.
typedef unspecified_type | Error_code
| The various errors detected by this package.

## Operations
Error_code | parameterize_border (Adaptor &mesh)
| Assign to mesh's border vertices a 2D position (i.e. a `(u, v)` pair) on border's shape. More...
bool | is_border_convex ()
| Indicate if border's shape is convex.

## Member Function Documentation

Error_code BorderParameterizer_3::parameterize_border | ( | Adaptor & | mesh) |  |

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

Mark them as parameterized. Return false on error.