Alpha complex data structure for 3d specific case. More...

Public Types
using	Alpha_shape_3 = CGAL::Alpha_shape_3< Dt >
	The CGAL 3D Alpha Shapes type. More...

using	FT = typename Alpha_shape_3::FT
	The alpha values type. Must be compatible with double.

using	Bare_point_3 = typename Kernel::Point_3
	Gives public access to the Bare_point_3 (bare aka. unweighed) type. Here is a Bare_point_3 constructor example: More...

using	Weighted_point_3 = typename Triangulation_3< Kernel, Tds, Weighted, Periodic >::Weighted_point_3
	Gives public access to the Weighted_point_3 type. A Weighted point can be constructed as follows: More...

using	Point_3 = typename Alpha_shape_3::Point
	`Alpha_complex_3d::Point_3` type is either a `Alpha_complex_3d::Bare_point_3` (Weighted = false) or a `Alpha_complex_3d::Weighted_point_3` (Weighted = true).

Public Member Functions
template<typename InputPointRange >
	Alpha_complex_3d (const InputPointRange &points)
	Alpha_complex constructor from a list of points. More...

template<typename InputPointRange , typename WeightRange >
	Alpha_complex_3d (const InputPointRange &points, WeightRange weights)
	Alpha_complex constructor from a list of points and associated weights. More...

template<typename InputPointRange >
	Alpha_complex_3d (const InputPointRange &points, FT x_min, FT y_min, FT z_min, FT x_max, FT y_max, FT z_max)
	Alpha_complex constructor from a list of points and an iso-cuboid coordinates. More...

template<typename InputPointRange , typename WeightRange >
	Alpha_complex_3d (const InputPointRange &points, WeightRange weights, FT x_min, FT y_min, FT z_min, FT x_max, FT y_max, FT z_max)
	Alpha_complex constructor from a list of points, associated weights and an iso-cuboid coordinates. More...

template<typename SimplicialComplexForAlpha3d , typename Filtration_value = typename SimplicialComplexForAlpha3d::Filtration_value>
bool	create_complex (SimplicialComplexForAlpha3d &complex, Filtration_value max_alpha_square=std::numeric_limits< Filtration_value >::infinity())
	Inserts all Delaunay triangulation into the simplicial complex. It also computes the filtration values accordingly to the Create complex algorithm. More...

const Point_3 &	get_point (std::size_t vertex)
	get_point returns the point corresponding to the vertex given as parameter. More...

Detailed Description

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>
class Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >

Alpha complex data structure for 3d specific case.

The data structure is constructing a CGAL 3D Alpha Shapes from a range of points (can be read from an OFF file, cf. Points_off_reader). Duplicate points are inserted once in the Alpha_complex.

Template Parameters

Complexity	shall be `Gudhi::alpha_complex::complexity` type. Default value is `Gudhi::alpha_complex::complexity::SAFE`.
Weighted	Boolean used to set/unset the weighted version of Alpha_complex_3d. Default value is false.
Periodic	Boolean used to set/unset the periodic version of Alpha_complex_3d. Default value is false.

For the weighted version, weights values are explained on CGAL Alpha shapes 3d and Regular triangulation documentation.

For the periodic version, refer to the CGAL’s 3D Periodic Triangulations User Manual for more details. The periodicity is defined by an iso-oriented cuboid with diagonal opposite vertices (x_min, y_min, z_min) and (x_max, y_max, z_max).

Please refer to Alpha complex for examples.

Remarks: When Alpha_complex_3d is constructed with an infinite value of alpha (default value), the complex is a 3d Delaunay complex.

Examples:: Alpha_complex/alpha_complex_3d_persistence.cpp, and Alpha_complex/Weighted_alpha_complex_3d_from_points.cpp.

Member Typedef Documentation

◆ Alpha_shape_3

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

using Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Alpha_shape_3 = CGAL::Alpha_shape_3<Dt>

The CGAL 3D Alpha Shapes type.

The Gudhi::alpha_complex::Alpha_complex_3d is a wrapper on top of this class to ease the standard, weighted and/or periodic build of the Alpha complex 3d.

◆ Bare_point_3

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

using Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Bare_point_3 = typename Kernel::Point_3

Gives public access to the Bare_point_3 (bare aka. unweighed) type. Here is a Bare_point_3 constructor example:

using Alpha_complex_3d = Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, false, false>;
// x0 = 1., y0 = -1.1, z0 = -1..
Alpha_complex_3d::Bare_point_3 p0(1., -1.1, -1.);

◆ Weighted_point_3

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

using Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Weighted_point_3 = typename Triangulation_3<Kernel, Tds, Weighted, Periodic>::Weighted_point_3

Gives public access to the Weighted_point_3 type. A Weighted point can be constructed as follows:

using Weighted_alpha_complex_3d = Gudhi::alpha_complex::Alpha_complex_3d<Gudhi::alpha_complex::complexity::SAFE, true, false>;
// x0 = 1., y0 = -1.1, z0 = -1., weight = 4.
Weighted_alpha_complex_3d::Weighted_point_3 wp0(Weighted_alpha_complex_3d::Bare_point_3(1., -1.1, -1.), 4.);

Note: This type is defined to void if Alpha complex is not weighted.

Constructor & Destructor Documentation

◆ Alpha_complex_3d() [1/4]

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

template<typename InputPointRange >

Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Alpha_complex_3d ( const InputPointRange & points )

inline

Alpha_complex constructor from a list of points.

Parameters

[in] points Range of points to triangulate. Points must be in Alpha_complex_3d::Point_3.

Precondition: Available if Alpha_complex_3d is not Periodic.

The type InputPointRange must be a range for which std::begin and std::end return input iterators on a Alpha_complex_3d::Point_3.

◆ Alpha_complex_3d() [2/4]

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

template<typename InputPointRange , typename WeightRange >

Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Alpha_complex_3d	(	const InputPointRange &	points,
		WeightRange	weights
	)

inline

Alpha_complex constructor from a list of points and associated weights.

Exceptions

std::invalid_argument In debug mode, if points and weights do not have the same size.

Parameters

[in]	points	Range of points to triangulate. Points must be in `Alpha_complex_3d::Bare_point_3`.
[in]	weights	Range of weights on points. Weights shall be in double.

Precondition: Available if Alpha_complex_3d is Weighted and not Periodic.

The type InputPointRange must be a range for which std::begin and std::end return input iterators on a Alpha_complex_3d::Bare_point_3. The type WeightRange must be a range for which std::begin and std::end return an input iterator on a double.

◆ Alpha_complex_3d() [3/4]

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

template<typename InputPointRange >

Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Alpha_complex_3d	(	const InputPointRange &	points,
		FT	x_min,
		FT	y_min,
		FT	z_min,
		FT	x_max,
		FT	y_max,
		FT	z_max
	)

inline

Alpha_complex constructor from a list of points and an iso-cuboid coordinates.

Exceptions

std::invalid_argument In debug mode, if the size of the cuboid in every directions is not the same.

Parameters

[in]	points	Range of points to triangulate. Points must be in `Alpha_complex_3d::Point_3`.
[in]	x_min	Iso-oriented cuboid x_min.
[in]	y_min	Iso-oriented cuboid y_min.
[in]	z_min	Iso-oriented cuboid z_min.
[in]	x_max	Iso-oriented cuboid x_max.
[in]	y_max	Iso-oriented cuboid y_max.
[in]	z_max	Iso-oriented cuboid z_max.

Precondition: Available if Alpha_complex_3d is Periodic.

The type InputPointRange must be a range for which std::begin and std::end return input iterators on a Alpha_complex_3d::Point_3.

Note: In weighted version, please check weights are greater than zero, and lower than 1/64*cuboid length squared.

◆ Alpha_complex_3d() [4/4]

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

template<typename InputPointRange , typename WeightRange >

Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::Alpha_complex_3d	(	const InputPointRange &	points,
		WeightRange	weights,
		FT	x_min,
		FT	y_min,
		FT	z_min,
		FT	x_max,
		FT	y_max,
		FT	z_max
	)

inline

Alpha_complex constructor from a list of points, associated weights and an iso-cuboid coordinates.

Exceptions

std::invalid_argument	In debug mode, if points and weights do not have the same size.
std::invalid_argument	In debug mode, if the size of the cuboid in every directions is not the same.
std::invalid_argument	In debug mode, if a weight is negative, zero, or greater than 1/64*cuboid length squared.

Parameters

[in]	points	Range of points to triangulate. Points must be in `Alpha_complex_3d::Bare_point_3`.
[in]	weights	Range of weights on points. Weights shall be in double.
[in]	x_min	Iso-oriented cuboid x_min.
[in]	y_min	Iso-oriented cuboid y_min.
[in]	z_min	Iso-oriented cuboid z_min.
[in]	x_max	Iso-oriented cuboid x_max.
[in]	y_max	Iso-oriented cuboid y_max.
[in]	z_max	Iso-oriented cuboid z_max.

Precondition: Available if Alpha_complex_3d is Weighted and Periodic.

The type InputPointRange must be a range for which std::begin and std::end return input iterators on a Alpha_complex_3d::Bare_point_3. The type WeightRange must be a range for which std::begin and std::end return an input iterator on a double. The type of x_min, y_min, z_min, x_max, y_max and z_max must be a double.

Member Function Documentation

◆ create_complex()

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

template<typename SimplicialComplexForAlpha3d , typename Filtration_value = typename SimplicialComplexForAlpha3d::Filtration_value>

bool Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::create_complex	(	SimplicialComplexForAlpha3d &	complex,
		Filtration_value	max_alpha_square = `std::numeric_limits<Filtration_value>::infinity()`
	)

inline

Inserts all Delaunay triangulation into the simplicial complex. It also computes the filtration values accordingly to the Create complex algorithm.

Template Parameters

SimplicialComplexForAlpha3d must meet SimplicialComplexForAlpha3d concept.

Parameters

[in]	complex	SimplicialComplexForAlpha3d to be created.
[in]	max_alpha_square	maximum for alpha square value. Default value is + \(\infty\), and there is very little point using anything else since it does not save time.

Returns: true if creation succeeds, false otherwise.

Precondition: The simplicial complex must be empty (no vertices).

◆ get_point()

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>

const Point_3& Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >::get_point ( std::size_t vertex )

inline

get_point returns the point corresponding to the vertex given as parameter.

Parameters

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

Returns: The point found.

Exceptions

std::out_of_range In case vertex is not found (cf. std::vector::at).

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

include/gudhi/Alpha_complex_3d.h

Public Types

Public Member Functions

Detailed Description

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false> class Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >

Member Typedef Documentation

◆ Alpha_shape_3

◆ Bare_point_3

◆ Weighted_point_3

Constructor & Destructor Documentation

◆ Alpha_complex_3d() [1/4]

◆ Alpha_complex_3d() [2/4]

◆ Alpha_complex_3d() [3/4]

◆ Alpha_complex_3d() [4/4]

Member Function Documentation

◆ create_complex()

◆ get_point()

template<complexity Complexity = complexity::SAFE, bool Weighted = false, bool Periodic = false>
class Gudhi::alpha_complex::Alpha_complex_3d< Complexity, Weighted, Periodic >