Approximation of Ridges and Umbilics on Triangulated Surface Meshes Reference

Todo:

check generated documentation

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-15a
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
template<class TriangulatedSurfaceMesh , class Vertex2FTPropertyMap , class Vertex2VectorPropertyMap , class OutputIterator >
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...
template<class TriangulatedSurfaceMesh , class Vertex2FTPropertyMap , class Vertex2VectorPropertyMap , class OutputIterator >
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. More...
template<class TriangulatedSurfaceMesh , class Vertex2FTPropertyMap , class Vertex2VectorPropertyMap , class OutputIterator >
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. More...
template<class TriangulatedSurfaceMesh , class Vertex2FTPropertyMap , class Vertex2VectorPropertyMap , class OutputIterator >
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. More...

Types
enum	CGAL::Ridge_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap >::Tag_order { CGAL::Ridge_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap >::Tag_3, CGAL::Ridge_approximation< TriangulatedSurfaceMesh, Vertex2FTPropertyMap, Vertex2VectorPropertyMap >::Tag_4 }
	Order of differential quantities used to distinguish elliptic and hyperbolic ridges. More...

Enumeration Type Documentation

template<typename TriangulatedSurfaceMesh , typename Vertex2FTPropertyMap , typename Vertex2VectorPropertyMap >

enum CGAL::Ridge_approximation::Tag_order

Order of differential quantities used to distinguish elliptic and hyperbolic ridges.

Third (Tag_3) or fourth (Tag_4) order quantities may be used as explained in section ridgemesh of the user manual.

Enumerator
Tag_3
Tag_4

Function Documentation

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

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.

The operator << is overloaded for this class and returns the line type, strength, sharpness and coordinates of the points of the polyline.

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

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.

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

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.

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

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.