Tangential complex data structure. More...

#include <gudhi/Tangential_complex.h>

Classes
struct	Fix_inconsistencies_info
	Type returned by `Tangential_complex::fix_inconsistencies_using_perturbation`. More...

struct	Num_inconsistencies
	Type returned by `Tangential_complex::number_of_inconsistent_simplices`. More...

Public Member Functions
template<typename Point_range >
	Tangential_complex (Point_range points, int intrinsic_dimension, const K &k=K())
	Constructor from a range of points. Points are copied into the instance, and a search data structure is initialized. Note the complex is not computed: `compute_tangential_complex` must be called after the creation of the object. More...

	~Tangential_complex ()
	Destructor.

int	intrinsic_dimension () const
	Returns the intrinsic dimension of the manifold.

int	ambient_dimension () const
	Returns the ambient dimension.

Point	get_point (std::size_t vertex) const
	Returns the point corresponding to the vertex given as parameter. More...

Point	get_perturbed_point (std::size_t vertex) const
	Returns the perturbed position of the point corresponding to the vertex given as parameter. More...

std::size_t	number_of_vertices () const
	Returns the number of vertices.

void	compute_tangential_complex ()
	Computes the tangential complex. More...

Fix_inconsistencies_info	fix_inconsistencies_using_perturbation (double max_perturb, double time_limit=-1.)
	Attempts to fix inconsistencies by perturbing the point positions. More...

Num_inconsistencies	number_of_inconsistent_simplices (bool verbose=false) const

template<typename Simplex_tree_ >
int	create_complex (Simplex_tree_ &tree, bool export_inconsistent_simplices=true) const
	Exports the complex into a Simplex_tree. More...

void	set_max_squared_edge_length (FT max_squared_edge_length)
	Sets the maximal possible squared edge length for the edges in the triangulations. More...

Detailed Description

template<typename Kernel_, typename DimensionTag, typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>
class Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >

Tangential complex data structure.

The class Tangential_complex represents a tangential complex. After the computation of the complex, an optional post-processing called perturbation can be run to attempt to remove inconsistencies.

Template Parameters

Kernel_	requires a CGAL::Epick_d class, which can be static if you know the ambiant dimension at compile-time, or dynamic if you don't.
DimensionTag	can be either Dimension_tag<d> if you know the intrinsic dimension at compile-time, or CGAL::Dynamic_dimension_tag if you don't.
Concurrency_tag	enables sequential versus parallel computation. Possible values are `CGAL::Parallel_tag` (the default) and `CGAL::Sequential_tag`.
Triangulation_	is the type used for storing the local regular triangulations. We highly recommend to use the default value (`CGAL::Regular_triangulation`).

Examples: example_basic.cpp, and example_with_perturb.cpp.

Constructor & Destructor Documentation

◆ Tangential_complex()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

template<typename Point_range >

Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::Tangential_complex	(	Point_range	points,
		int	intrinsic_dimension,
		const K &	k = `K()`
	)

inline

Constructor from a range of points. Points are copied into the instance, and a search data structure is initialized. Note the complex is not computed: compute_tangential_complex must be called after the creation of the object.

Parameters

[in]	points	Range of points (`Point_range::value_type` must be the same as `Kernel_::Point_d`).
[in]	intrinsic_dimension	Intrinsic dimension of the manifold.
[in]	k	Kernel instance.

Member Function Documentation

◆ compute_tangential_complex()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

void Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::compute_tangential_complex ( )

inline

Computes the tangential complex.

Exceptions

std::invalid_argument In debug mode, if the computed star dimension is too low. Try to set a bigger maximal edge length value with Tangential_complex::set_max_squared_edge_length if this happens.

Examples: example_basic.cpp, and example_with_perturb.cpp.

◆ create_complex()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

template<typename Simplex_tree_ >

int Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::create_complex	(	Simplex_tree_ &	tree,
		bool	export_inconsistent_simplices = `true`
	)		const

inline

Exports the complex into a Simplex_tree.

Template Parameters

Simplex_tree_ must be a Simplex_tree.

Parameters

[out]	tree	The result, where each `Vertex_handle` is the index of the corresponding point in the range provided to the constructor (it can also be retrieved through the `Tangential_complex::get_point` function.
[in]	export_inconsistent_simplices	Also export inconsistent simplices or not?

Returns: The maximal dimension of the simplices.

Examples: example_basic.cpp, and example_with_perturb.cpp.

◆ fix_inconsistencies_using_perturbation()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

Fix_inconsistencies_info Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::fix_inconsistencies_using_perturbation	(	double	max_perturb,
		double	time_limit = `-1.`
	)

inline

Attempts to fix inconsistencies by perturbing the point positions.

Parameters

[in]	max_perturb	Maximum length of the translations used by the perturbation.
[in]	time_limit	Time limit in seconds. If -1, no time limit is set.

Examples: example_with_perturb.cpp.

◆ get_perturbed_point()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

Point Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::get_perturbed_point ( std::size_t vertex ) const

inline

Returns the perturbed position of the point corresponding to the vertex given as parameter.

Parameters

[in] vertex Vertex handle of the point to retrieve.

Returns: The perturbed position of the point found.

◆ get_point()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

Point Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::get_point ( std::size_t vertex ) const

inline

Returns the point corresponding to the vertex given as parameter.

Parameters

[in] vertex Vertex handle of the point to retrieve.

Returns: The point found.

◆ number_of_inconsistent_simplices()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

Num_inconsistencies Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::number_of_inconsistent_simplices ( bool verbose = false ) const

inline

Returns the number of inconsistencies

Parameters

[in] verbose If true, outputs a message into std::cerr.

Examples: example_basic.cpp.

◆ set_max_squared_edge_length()

template<typename Kernel_ , typename DimensionTag , typename Concurrency_tag = CGAL::Parallel_tag, typename Triangulation_ = CGAL::Default>

void Gudhi::tangential_complex::Tangential_complex< Kernel_, DimensionTag, Concurrency_tag, Triangulation_ >::set_max_squared_edge_length ( FT max_squared_edge_length )

inline

Sets the maximal possible squared edge length for the edges in the triangulations.

Parameters

[in] max_squared_edge_length Maximal possible squared edge length.

If the maximal edge length value is too low Tangential_complex::compute_tangential_complex will throw an exception in debug mode.

The documentation for this class was generated from the following file:

include/gudhi/Tangential_complex.h

Classes

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Tangential_complex()

Member Function Documentation

◆ compute_tangential_complex()

◆ create_complex()

◆ fix_inconsistencies_using_perturbation()

◆ get_perturbed_point()

◆ get_point()

◆ number_of_inconsistent_simplices()

◆ set_max_squared_edge_length()