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: CGAL and Solvers
BibTeX: cgal:cp-arutsm-16a
License: GPL

Classified Reference Pages

Enums

• CGAL::Ridge_type
• CGAL::Ridge_order
• CGAL::Umbilic_type

Classes

• CGAL::Ridge_line<TriangleMesh>
• CGAL::Umbilic<TriangleMesh>
• CGAL::Ridge_approximation<TriangleMesh,VertexFTMap,VertexVectorMap>
• CGAL::Umbilic_approximation<TriangleMesh,VertexFTMap,VertexVectorMap>

Global Functions

• CGAL::compute_max_ridges()
• CGAL::compute_min_ridges()
• CGAL::compute_crest_ridges()
• CGAL::compute_umbilics()

Modules
	Enums

Classes
class	CGAL::Ridge_approximation< TriangleMesh, VertexFTMap, VertexVectorMap >
	The class Ridge_approximation computes the approximation of ridges of a triangular polyhedral surface. More...
class	CGAL::Ridge_line< TriangleMesh >
	The class Ridge_line stores the description of a ridge line. More...
class	CGAL::Umbilic_approximation< TriangleMesh, VertexFTMap, VertexVectorMap >
	The class Umbilic_approximation computes the approximation of umbilics on a triangular polyhedral surface. More...
class	CGAL::Umbilic< TriangleMesh >
	The class Umbilic stores the description of an umbilic. More...

Functions
template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >
OutputIterator	CGAL::compute_crest_ridges (const TriangleMesh &tm, VertexFTMap vertex_k1_pm, VertexFTMap vertex_k2_pm, VertexFTMap vertex_b0_pm, VertexFTMap vertex_b3_pm, VertexVectorMap vertex_d1_pm, VertexVectorMap vertex_d2_pm, VertexFTMap vertex_P1_pm, VertexFTMap vertex_P2_pm, OutputIterator it, CGAL::Ridge_order order=CGAL::Ridge_order_3)
	The function compute_crest_ridges() is a shortcut to the method Ridge_approximation::compute_crest_ridges(). More...
template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >
OutputIterator	CGAL::compute_max_ridges (const TriangleMesh &tm, VertexFTMap vertex_k1_pm, VertexFTMap vertex_k2_pm, VertexFTMap vertex_b0_pm, VertexFTMap vertex_b3_pm, VertexVectorMap vertex_d1_pm, VertexVectorMap vertex_d2_pm, VertexFTMap vertex_P1_pm, const VertexFTMap vertex_P2_pm, OutputIterator it, CGAL::Ridge_order order=CGAL::Ridge_order_3)
	The function compute_max_ridges() is a shortcut to the method Ridge_approximation::compute_max_ridges(). More...
template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >
OutputIterator	CGAL::compute_min_ridges (const TriangleMesh &tm, VertexFTMap vertex_k1_pm, VertexFTMap vertex_k2_pm, VertexFTMap vertex_b0_pm, VertexFTMap vertex_b3_pm, VertexVectorMap vertex_d1_pm, VertexVectorMap vertex_d2_pm, VertexFTMap vertex_P1_pm, VertexFTMap vertex_P2_pm, OutputIterator it, CGAL::Ridge_order order=CGAL::Ridge_order_3)
	The function compute_min_ridges() is a shortcut to the method Ridge_approximation::compute_min_ridges(). More...
template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >
OutputIterator	CGAL::compute_umbilics (const TriangleMesh &tm, VertexFTMap vertex_k1_pm, VertexFTMap vertex_k2_pm, VertexVectorMap vertex_d1_pm, VertexVectorMap vertex_d2_pm, OutputIterator it, double size)
	The function compute_umbilics() is a shortcut to the method Umbilic_approximation::compute(). More...

Function Documentation

template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >

OutputIterator CGAL::compute_crest_ridges	(	const TriangleMesh &	tm,
		VertexFTMap	vertex_k1_pm,
		VertexFTMap	vertex_k2_pm,
		VertexFTMap	vertex_b0_pm,
		VertexFTMap	vertex_b3_pm,
		VertexVectorMap	vertex_d1_pm,
		VertexVectorMap	vertex_d2_pm,
		VertexFTMap	vertex_P1_pm,
		VertexFTMap	vertex_P2_pm,
		OutputIterator	it,
		CGAL::Ridge_order	order = CGAL::Ridge_order_3
	)

The function compute_crest_ridges() is a shortcut to the method Ridge_approximation::compute_crest_ridges().

See Ridge_approximation::Ridge_approximation() for an explanation of the parameters.

#include <CGAL/Ridges.h>

template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >

OutputIterator CGAL::compute_max_ridges	(	const TriangleMesh &	tm,
		VertexFTMap	vertex_k1_pm,
		VertexFTMap	vertex_k2_pm,
		VertexFTMap	vertex_b0_pm,
		VertexFTMap	vertex_b3_pm,
		VertexVectorMap	vertex_d1_pm,
		VertexVectorMap	vertex_d2_pm,
		VertexFTMap	vertex_P1_pm,
		const VertexFTMap	vertex_P2_pm,
		OutputIterator	it,
		CGAL::Ridge_order	order = CGAL::Ridge_order_3
	)

The function compute_max_ridges() is a shortcut to the method Ridge_approximation::compute_max_ridges().

See Ridge_approximation::Ridge_approximation() for an explanation of the parameters.

#include <CGAL/Ridges.h>

template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >

OutputIterator CGAL::compute_min_ridges	(	const TriangleMesh &	tm,
		VertexFTMap	vertex_k1_pm,
		VertexFTMap	vertex_k2_pm,
		VertexFTMap	vertex_b0_pm,
		VertexFTMap	vertex_b3_pm,
		VertexVectorMap	vertex_d1_pm,
		VertexVectorMap	vertex_d2_pm,
		VertexFTMap	vertex_P1_pm,
		VertexFTMap	vertex_P2_pm,
		OutputIterator	it,
		CGAL::Ridge_order	order = CGAL::Ridge_order_3
	)

The function compute_min_ridges() is a shortcut to the method Ridge_approximation::compute_min_ridges().

See Ridge_approximation::Ridge_approximation() for an explanation of the parameters.

#include <CGAL/Ridges.h>

template<class TriangleMesh , class VertexFTMap , class VertexVectorMap , class OutputIterator >

OutputIterator CGAL::compute_umbilics	(	const TriangleMesh &	tm,
		VertexFTMap	vertex_k1_pm,
		VertexFTMap	vertex_k2_pm,
		VertexVectorMap	vertex_d1_pm,
		VertexVectorMap	vertex_d2_pm,
		OutputIterator	it,
		double	size
	)

The function compute_umbilics() is a shortcut to the method Umbilic_approximation::compute().

See Umbilic_approximation::Umbilic_approximation() for an explanation of the parameters.

#include <CGAL/Umbilics.h>