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

CGAL 4.3 - Approximation of Ridges and Umbilics on Triangulated Surface Meshes

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Approximation of Ridges and Umbilics on Triangulated Surface Meshes Reference

##

Marc Pouget and Frédéric Cazals
Global features related to curvature extrema encode important informations used in segmentation, registration, matching and surface analysis. Given pointwise estimations of local differential quantities, this package allows the approximation of differential features on a triangulated surface mesh. Such curvature related features are curves: ridges or crests, and points: umbilics.

Introduced in: CGAL 3.3
Depends on: Solvers from Eigen.
BibTeX: cgal:cp-arutsm-13b
License: GPL

## Classified Reference Pages

## Concepts

- `TriangulatedSurfaceMesh`
- `Vertex2FTPropertyMap`
- `Vertex2VectorPropertyMap`

## Enums

- `CGAL::Ridge_type`
- `CGAL::Ridge_order`
- `CGAL::Umbilic_type`

## Classes

- `CGAL::Ridge_line<TriangulatedSurfaceMesh>`
- `CGAL::Umbilic<TriangulatedSurfaceMesh>`
- `CGAL::Ridge_approximation<TriangulatedSurfaceMesh,Vertex2FTPropertyMap,Vertex2VectorPropertyMap>`
- `CGAL::Umbilic_approximation<TriangulatedSurfaceMesh,Vertex2FTPropertyMap,Vertex2VectorPropertyMap>`

## Global Functions

- `CGAL::compute_max_ridges()`
- `CGAL::compute_min_ridges()`
- `CGAL::compute_crest_ridges()`
- `CGAL::compute_umbilics()`

## Modules
| Concepts
| Enums

## Classes
class | CGAL::Ridge_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap >
| The class `Ridge_approximation` computes the approximation of ridges of a triangular polyhedral surface. More...
class | CGAL::Ridge_line< TriangulatedSurfaceMesh >
| The class `Ridge_line` stores the description of a ridge line. More...
class | CGAL::Vertex2Data_Property_Map_with_std_map< TriangulatedSurfaceMesh >
| The class `Vertex2Data_Property_Map_with_std_map` is a model of the concepts `Vertex2FTPropertyMap` and `Vertex2VectorPropertyMap` to be used for `Ridge_approximation`. More...
struct | CGAL::Vertex2Data_Property_Map_with_std_map< TriangulatedSurfaceMesh >::Vertex_cmp
class | CGAL::Umbilic_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap >
| The class `Umbilic_approximation` computes the approximation of umbilics on a triangular polyhedral surface. More...
class | CGAL::Umbilic< TriangulatedSurfaceMesh >
| The class `Umbilic` stores the description of an umbilic. More...

## Functions
OutputIterator | CGAL::compute_crest_ridges (const TriangulatedSurfaceMesh &P, const Vertex2FTPropertyMap &vertex2k1_pm, const Vertex2FTPropertyMap &vertex2k2_pm, const Vertex2FTPropertyMap &vertex2b0_pm, const Vertex2FTPropertyMap &vertex2b3_pm, const Vertex2VectorPropertyMap &vertex2d1_pm, const Vertex2VectorPropertyMap &vertex2d2_pm, const Vertex2FTPropertyMap &vertex2P1_pm, const Vertex2FTPropertyMap &vertex2P2_pm, OutputIterator it, CGAL::Ridge_order order=CGAL::Ridge_order_3)
| The function `compute_crest_ridges()` is a shortcut to the method of the same name of the class `Ridge_approximation`. More...
OutputIterator | CGAL::compute_max_ridges (const TriangulatedSurfaceMesh &P, const Vertex2FTPropertyMap &vertex2k1_pm, const Vertex2FTPropertyMap &vertex2k2_pm, const Vertex2FTPropertyMap &vertex2b0_pm, const Vertex2FTPropertyMap &vertex2b3_pm, const Vertex2VectorPropertyMap &vertex2d1_pm, const Vertex2VectorPropertyMap &vertex2d2_pm, const Vertex2FTPropertyMap &vertex2P1_pm, const Vertex2FTPropertyMap &vertex2P2_pm, OutputIterator it, CGAL::Ridge_order order=CGAL::Ridge_order_3)
| The function `compute_max_ridges()` is a shortcut to the method of the same name of the class `Ridge_approximation`.
OutputIterator | CGAL::compute_min_ridges (const TriangulatedSurfaceMesh &P, const Vertex2FTPropertyMap &vertex2k1_pm, const Vertex2FTPropertyMap &vertex2k2_pm, const Vertex2FTPropertyMap &vertex2b0_pm, const Vertex2FTPropertyMap &vertex2b3_pm, const Vertex2VectorPropertyMap &vertex2d1_pm, const Vertex2VectorPropertyMap &vertex2d2_pm, const Vertex2FTPropertyMap &vertex2P1_pm, const Vertex2FTPropertyMap &vertex2P2_pm, OutputIterator it, CGAL::Ridge_order order=CGAL::Ridge_order_3)
| The function `compute_min_ridges()` is a shortcut to the method of the same name of the class `Ridge_approximation`.
OutputIterator | CGAL::compute_umbilics (const TriangulatedSurfaceMesh &P, const Vertex2FTPropertyMap &vertex2k1_pm, const Vertex2FTPropertyMap &vertex2k2_pm, const Vertex2VectorPropertyMap &vertex2d1_pm, const Vertex2VectorPropertyMap &vertex2d2_pm, OutputIterator it, double size)
| The function `compute_umbilics()` is a shortcut to the method `compute()` of the class `Umbilic_approximation`.