\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11 - Planar Parameterization of Triangulated Surface Meshes
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Triangulated Surface Mesh Parameterization Reference

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Laurent Saboret, Pierre Alliez, Bruno Lévy, Mael Rouxel-Labbé, and Andreas Fabri
Parameterizing a surface amounts to finding a one-to-one mapping from a suitable domain to the surface. In this package, we focus on triangulated surfaces that are homeomorphic to a disk and on piecewise linear mappings into a planar domain. This package implements several surface mesh parameterization methods, such as As Rigid As Possible Parameterization, Discrete Authalic Parameterization, Discrete Conformal Map, Floater Mean Value Coordinates, Least Squares Conformal Maps, Orbifold Tutte Embedding, or Tutte Barycentric Mapping. The code is generic and works with any model of the FaceListGraph concept.


Introduced in: CGAL 3.2
Depends on: CGAL and Solvers
BibTeX: cgal:salf-pptsm2-17b
License: GPL
Windows Demo: Polyhedron demo
Common Demo Dlls: dlls

Classified Reference Pages

Main Function

Concepts

Surface Parameterization Methods

This CGAL package implements several parameterization methods:

The following classes implement the methods listed above:

Border Parameterization Methods

Border parameterization methods define a set of constraints (a constraint specifies two (u,v) coordinates for each instance of a vertex along the border).

This package implements common border parameterization methods:

The following classes implement the methods listed above:

Mesh

The general definition of input meshes handled directly by CGAL::Surface_mesh_parameterization::parameterize() is a triangulated surface mesh model of FaceGraph that is homeomorphic to a disc (may have holes). In particular, it means that it must be 2-manifold and oriented.

Checks and Assertions

The package performs the next checks:

Modules

 Main Function
 
 Enums
 
 Concepts
 
 Surface Parameterization Methods
 This CGAL package implements several parameterization methods:
 
 Border Parameterization Methods
 Border parameterization methods define a set of constraints (a constraint specifies two (u,v) coordinates for each instance of a vertex along the border).