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

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

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CGAL::Umbilic_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap > Class Template Reference
Approximation of Ridges and Umbilics on Triangulated Surface Meshes Reference

`#include <CGAL/Umbilics.h>`

## Definition

The class `Umbilic_approximation` computes the approximation of umbilics on a triangular polyhedral surface.

Template Parameters

  TriangulatedSurfaceMesh | is the surface type.
  Vertex2FTPropertyMap,Vertex2VectorPropertyMap | provide the differential properties of the surface associated to its vertices.

Requirements (checked at compile time) :

- the types `TriangulatedSurfaceMesh::Traits::FT` and `Vertex2FTPropertyMap::value_type` must coincide;
- the types `TriangulatedSurfaceMesh::Traits::Vector_3` and `Vertex2VectorPropertyMap::value_type` must coincide;
- the types `TriangulatedSurfaceMesh::Vertex_handle`, `Vertex2FTPropertyMap::key_type` and `Vertex2VectorPropertyMap::key_type` must coincide;

See Also
  `Umbilic`
  `TriangulatedSurfaceMesh`
  `Vertex2FTPropertyMap`
  `Vertex2VectorPropertyMap`

## Types
typedef TriangulatedSurfaceMesh::Traits::FT | FT

## Creation
| Umbilic_approximation (const TriangulatedSurfaceMesh &P, const Vertex2FTPropertyMap &vertex2k1_pm, const Vertex2FTPropertyMap &vertex2k2_pm, const Vertex2VectorPropertyMap &vertex2d1_pm, const Vertex2VectorPropertyMap &vertex2d2_pm)
| default constructor.

## Operations
template<class OutputIterator >
OutputIterator | compute (OutputIterator it, FT size)
| Performs the approximation, `size` determines the size of the patches around vertices, taken as `size` times the size of the 1-ring. More...

## Member Function Documentation

template<typename TriangulatedSurfaceMesh , typename Vertex2FTPropertyMap , typename Vertex2VectorPropertyMap >
template<class OutputIterator >

OutputIterator CGAL::Umbilic_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap >::compute | ( | OutputIterator | it,
|  | FT | size
| ) |  |

Performs the approximation, `size` determines the size of the patches around vertices, taken as `size` times the size of the 1-ring.

Umbilics are inserted into the `OutputIterator` `it` with value type `Umbilic*`.