Create foliated spherical triangulations. More...

#include "Triangulation_traits.hpp"
#include "Utilities.hpp"

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Classes
class	foliated_triangulations::FoliatedTriangulation< 3 >
	3D Foliated triangulation More...

class	foliated_triangulations::FoliatedTriangulation< 4 >
	4D Triangulation More...

Concepts
concept	ContainerType
	This is std::movable from <concepts>

Typedefs
template<int dimension>
using	Causal_vertices_t = std::vector< std::pair< Point_t< dimension >, Int_precision > >

template<int dimension>
using	Cell_handle_t = typename TriangulationTraits< dimension >::Cell_handle

template<int dimension>
using	Delaunay_t = typename TriangulationTraits< dimension >::Delaunay

template<int dimension>
using	Edge_handle_t = typename TriangulationTraits< dimension >::Edge_handle

template<int dimension>
using	Face_handle_t = typename TriangulationTraits< dimension >::Face_handle

template<int dimension>
using	Facet_t = typename TriangulationTraits< dimension >::Facet

using	foliated_triangulations::FoliatedTriangulation_3 = FoliatedTriangulation< 3 >

using	foliated_triangulations::FoliatedTriangulation_4 = FoliatedTriangulation< 4 >

template<int dimension>
using	Point_t = typename TriangulationTraits< dimension >::Point

template<int dimension>
using	Spherical_points_generator_t = typename TriangulationTraits< dimension >::Spherical_points_generator

template<int dimension>
using	Vertex_handle_t = typename TriangulationTraits< dimension >::Vertex_handle

Enumerations
enum class	Cell_type { THREE_ONE = 31 , TWO_TWO = 22 , ONE_THREE = 13 , FOUR_ONE = 41 , THREE_TWO = 32 , TWO_THREE = 23 , ONE_FOUR = 14 , ACAUSAL = 99 , UNCLASSIFIED = 0 }
	(n,m) is number of vertices on (lower, higher) timeslice More...

Functions
template<int dimension>
auto	foliated_triangulations::check_cells (Delaunay_t< dimension > const &t_triangulation) -> bool
	Check all finite cells in the Delaunay triangulation.

template<int dimension>
auto	foliated_triangulations::check_timevalues (Delaunay_t< dimension > const &t_triangulation) -> std::optional< std::vector< Cell_handle_t< dimension > > >
	Check cells for correct foliation.

template<int dimension>
auto	foliated_triangulations::check_vertices (Delaunay_t< dimension > const &t_triangulation, double t_initial_radius, double t_foliation_spacing)
	Check if vertices have the correct timevalues.

template<int dimension>
auto	foliated_triangulations::classify_edge (Edge_handle_t< dimension > const &t_edge) -> bool
	Predicate to classify edge as timelike or spacelike.

template<int dimension>
auto	foliated_triangulations::collect_cells (Delaunay_t< dimension > const &t_triangulation) -> std::vector< Cell_handle_t< dimension > >
	Obtain all finite cells in the Delaunay triangulation.

template<int dimension>
auto	foliated_triangulations::collect_edges (Delaunay_t< dimension > const &delaunay)
	Returns a container of all the finite edges in the triangulation.

template<int dimension>
auto	foliated_triangulations::collect_vertices (Delaunay_t< dimension > const &t_triangulation)
	Obtain all finite vertices in the Delaunay triangulation.

template<int dimension, ContainerType Container>
void	foliated_triangulations::debug_print_cells (Container &&t_cells)
	Write to debug log timevalues of each vertex in the cell and the resulting cell->info.

template<int dimension>
auto	foliated_triangulations::expected_cell_type (Cell_handle_t< dimension > const &t_cell)
	Classifies cells by their timevalues.

template<int dimension>
auto	foliated_triangulations::expected_timevalue (Vertex_handle_t< dimension > const &t_vertex, double t_initial_radius, double t_foliation_spacing) -> Int_precision
	Find the expected timevalue for a vertex.

template<int dimension>
auto	foliated_triangulations::filter_cells (std::vector< Cell_handle_t< dimension > > const &t_cells, Cell_type const &t_cell_type) -> std::vector< Cell_handle_t< dimension > >

template<int dimension>
auto	foliated_triangulations::filter_edges (std::vector< Edge_handle_t< dimension > > const &t_edges, bool t_is_Timelike_pred) -> std::vector< Edge_handle_t< dimension > >

template<int dimension>
auto	foliated_triangulations::find_bad_vertex (Cell_handle_t< dimension > const &cell) -> Vertex_handle_t< dimension >
	Find the vertex that is causing a cell's foliation to be invalid.

template<int dimension>
auto	foliated_triangulations::find_cell (Delaunay_t< dimension > const &delaunay, Vertex_handle_t< dimension > const &vh1, Vertex_handle_t< dimension > const &vh2, Vertex_handle_t< dimension > const &vh3, Vertex_handle_t< dimension > const &vh4) -> std::optional< Cell_handle_t< dimension > >
	Returns the cell containing the vertices.

template<int dimension>
auto	foliated_triangulations::find_incorrect_cells (Delaunay_t< dimension > const &t_triangulation)
	Check all finite cells in the Delaunay triangulation.

template<int dimension>
auto	foliated_triangulations::find_incorrect_vertices (Delaunay_t< dimension > const &t_triangulation, double t_initial_radius, double t_foliation_spacing)
	Obtain vertices with incorrect timevalues.

template<int dimension>
auto	foliated_triangulations::find_incorrect_vertices (std::vector< Cell_handle_t< dimension > > const &t_cells, double t_initial_radius, double t_foliation_spacing)
	Obtain vertices with incorrect timevalues.

template<int dimension, ContainerType Container>
auto	foliated_triangulations::find_max_timevalue (Container &&t_vertices) -> Int_precision

template<int dimension, ContainerType Container>
auto	foliated_triangulations::find_min_timevalue (Container &&t_vertices) -> Int_precision

template<int dimension>
auto	foliated_triangulations::find_vertex (Delaunay_t< dimension > const &delaunay, Point_t< dimension > const &point) -> std::optional< Vertex_handle_t< dimension > >
	Returns the vertex containing the given point.

template<int dimension>
auto	foliated_triangulations::fix_cells (Delaunay_t< dimension > const &t_triangulation) -> bool
	Fix simplices with the wrong type.

template<int dimension>
auto	foliated_triangulations::fix_timevalues (Delaunay_t< dimension > &t_triangulation) -> bool
	Fix the vertices of a cell to be consistent with the foliation.

template<int dimension>
auto	foliated_triangulations::fix_vertices (Delaunay_t< dimension > const &t_triangulation, double const t_initial_radius, double const t_foliation_spacing) -> bool
	Fix vertices with incorrect timevalues.

template<int dimension>
auto	foliated_triangulations::fix_vertices (std::vector< Cell_handle_t< dimension > > const &t_cells, double t_initial_radius, double t_foliation_spacing)
	Fix vertices with incorrect timevalues.

template<int dimension>
auto	foliated_triangulations::get_vertices_from_cells (std::vector< Cell_handle_t< dimension > > const &t_cells)
	Extracts vertices from cells.

template<int dimension>
auto	foliated_triangulations::is_cell_type_correct (Cell_handle_t< dimension > const &t_cell) -> bool
	Checks if a cell is classified correctly.

template<int dimension>
auto	foliated_triangulations::is_vertex_timevalue_correct (Vertex_handle_t< dimension > const &t_vertex, double const t_initial_radius, double const t_foliation_spacing) -> bool
	Checks if vertex timevalue is correct.

template<int dimension>
auto	foliated_triangulations::make_causal_vertices (std::span< Point_t< dimension > const > vertices, std::span< size_t const > timevalues) -> Causal_vertices_t< dimension >
	Create causal vertices from vertices and timevalues.

template<int dimension>
auto	foliated_triangulations::make_foliated_ball (Int_precision const t_simplices, Int_precision const t_timeslices, double const initial_radius=INITIAL_RADIUS, double const foliation_spacing=FOLIATION_SPACING)
	Make foliated ball.

template<int dimension>
auto	foliated_triangulations::make_triangulation (Int_precision const t_simplices, Int_precision t_timeslices, double const initial_radius=INITIAL_RADIUS, double const foliation_spacing=FOLIATION_SPACING) -> Delaunay_t< dimension >
	Make a Delaunay triangulation.

template<int dimension>
void	foliated_triangulations::print_cell (Cell_handle_t< dimension > cell)
	Print a cell in the triangulation.

template<int dimension, typename Container >
void	foliated_triangulations::print_cells (Container &&t_cells)
	Print timevalues of each vertex in the cell and the resulting cell->info()

template<int dimension>
void	foliated_triangulations::print_edge (Edge_handle_t< dimension > const &t_edge)
	Print edge.

template<int dimension>
void	foliated_triangulations::print_neighboring_cells (Cell_handle_t< dimension > cell)
	Print neighboring cells.

template<int dimension>
auto	foliated_triangulations::squared_radius (Vertex_handle_t< dimension > const &t_vertex) -> double
	Calculate the squared radius from the origin.

template<int dimension, ContainerType Container>
auto	foliated_triangulations::volume_per_timeslice (Container &&t_facets) -> std::multimap< Int_precision, Facet_t< 3 > >
	Collect spacelike facets into a container indexed by time value.

Variables
template<int dimension>
auto constexpr	foliated_triangulations::compare_v_info

static int constexpr	foliated_triangulations::MAX_FIX_PASSES = 50

Detailed Description

Create foliated spherical triangulations.

Author: Adam Getchell

Extends CGAL's Delaunay_triangulation_3 and Triangulation_3 classes to create foliated spherical triangulations of a given dimension.

The dimensionality, number of desired simplices, and number of desired timeslices is given. Successive spheres are created with increasing radii, parameterized by INITIAL_RADIUS and RADIAL_FACTOR. Each vertex at a given radius is assigned a timeslice so that the entire triangulation will have a defined foliation of time.

See also: https://doc.cgal.org/latest/Triangulation_3/index.html#Chapter_3D_Triangulations

Definition in file Foliated_triangulation.hpp.

Typedef Documentation

◆ Causal_vertices_t

template<int dimension>

using Causal_vertices_t = std::vector<std::pair<Point_t<dimension>, Int_precision> >

Definition at line 34 of file Foliated_triangulation.hpp.

◆ Cell_handle_t

template<int dimension>

using Cell_handle_t = typename TriangulationTraits<dimension>::Cell_handle

Definition at line 38 of file Foliated_triangulation.hpp.

◆ Delaunay_t

template<int dimension>

using Delaunay_t = typename TriangulationTraits<dimension>::Delaunay

Definition at line 28 of file Foliated_triangulation.hpp.

◆ Edge_handle_t

template<int dimension>

using Edge_handle_t = typename TriangulationTraits<dimension>::Edge_handle

Definition at line 47 of file Foliated_triangulation.hpp.

◆ Face_handle_t

template<int dimension>

using Face_handle_t = typename TriangulationTraits<dimension>::Face_handle

Definition at line 41 of file Foliated_triangulation.hpp.

◆ Facet_t

template<int dimension>

using Facet_t = typename TriangulationTraits<dimension>::Facet

Definition at line 44 of file Foliated_triangulation.hpp.

◆ FoliatedTriangulation_3

using foliated_triangulations::FoliatedTriangulation_3 = typedef FoliatedTriangulation<3>

Definition at line 1577 of file Foliated_triangulation.hpp.

◆ FoliatedTriangulation_4

using foliated_triangulations::FoliatedTriangulation_4 = typedef FoliatedTriangulation<4>

Definition at line 1584 of file Foliated_triangulation.hpp.

◆ Point_t

template<int dimension>

using Point_t = typename TriangulationTraits<dimension>::Point

Definition at line 31 of file Foliated_triangulation.hpp.

◆ Spherical_points_generator_t

template<int dimension>

using Spherical_points_generator_t = typename TriangulationTraits<dimension>::Spherical_points_generator

Definition at line 53 of file Foliated_triangulation.hpp.

◆ Vertex_handle_t

template<int dimension>

using Vertex_handle_t = typename TriangulationTraits<dimension>::Vertex_handle

Definition at line 50 of file Foliated_triangulation.hpp.

Enumeration Type Documentation

◆ Cell_type

enum class Cell_type

strong

(n,m) is number of vertices on (lower, higher) timeslice

Definition at line 64 of file Foliated_triangulation.hpp.

Function Documentation

◆ check_cells()

template<int dimension>

auto foliated_triangulations::check_cells ( Delaunay_t< dimension > const & t_triangulation ) -> bool

Check all finite cells in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: True if there are no finite cells, or all finite cells are correctly classified

Definition at line 584 of file Foliated_triangulation.hpp.

References foliated_triangulations::check_cells().

Referenced by foliated_triangulations::check_cells().

◆ check_timevalues()

template<int dimension>

auto foliated_triangulations::check_timevalues ( Delaunay_t< dimension > const & t_triangulation ) -> std::optional<std::vector<Cell_handle_t<dimension>>>

Check cells for correct foliation.

The timevalues of the vertices of a cell differ by at most one and cannot all be the same. The first case would correspond to the cell (simplex) spanning more than one timeslice; the second would correspond to the cell being purely spacelike. Both of these cases are causally inconsistent. Note that this takes a Delaunay triangulation as input, as it is expected to be called while the Foliated triangulation is still being constructed. Note also that to guard against numeric errors causing invalid cells, fix_vertices() should be called before this function.

Template Parameters

dimension The dimensionality of the cells and triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: An optional container of invalid cells

Definition at line 787 of file Foliated_triangulation.hpp.

References foliated_triangulations::check_timevalues().

Referenced by foliated_triangulations::check_timevalues().

◆ check_vertices()

template<int dimension>

auto foliated_triangulations::check_vertices	(	Delaunay_t< dimension > const &	t_triangulation,
		double	t_initial_radius,
		double	t_foliation_spacing
	)

Check if vertices have the correct timevalues.

Template Parameters

dimension Dimensionality of the vertices and Delaunay triangulation

Parameters

t_triangulation	The Delaunay triangulation
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: True if all vertices have correct timevalues

Definition at line 367 of file Foliated_triangulation.hpp.

References foliated_triangulations::check_vertices().

Referenced by foliated_triangulations::check_vertices().

◆ classify_edge()

template<int dimension>

auto foliated_triangulations::classify_edge ( Edge_handle_t< dimension > const & t_edge ) -> bool

Predicate to classify edge as timelike or spacelike.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_edge The Edge_handle to classify

Returns: True if timelike and false if spacelike

Definition at line 227 of file Foliated_triangulation.hpp.

References foliated_triangulations::classify_edge().

Referenced by foliated_triangulations::classify_edge().

◆ collect_cells()

template<int dimension>

auto foliated_triangulations::collect_cells ( Delaunay_t< dimension > const & t_triangulation ) -> std::vector<Cell_handle_t<dimension>>

Obtain all finite cells in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The triangulation

Returns: A container of finite cells

Definition at line 384 of file Foliated_triangulation.hpp.

References foliated_triangulations::collect_cells().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::collect_cells().

◆ collect_edges()

template<int dimension>

auto foliated_triangulations::collect_edges ( Delaunay_t< dimension > const & delaunay )

Returns a container of all the finite edges in the triangulation.

Regardless of the dimensionality of the triangulation, the edges are 1-d simplices connecting 0-d vertices.

Template Parameters

dimension The dimensionality of the triangulation

Parameters

delaunay The triangulation

Returns: Container of all the finite edges in the triangulation

Definition at line 114 of file Foliated_triangulation.hpp.

References foliated_triangulations::collect_edges().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::collect_edges().

◆ collect_vertices()

template<int dimension>

auto foliated_triangulations::collect_vertices ( Delaunay_t< dimension > const & t_triangulation )

Obtain all finite vertices in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: A container of finite vertices

Definition at line 345 of file Foliated_triangulation.hpp.

References foliated_triangulations::collect_vertices().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::collect_vertices().

◆ debug_print_cells()

template<int dimension, ContainerType Container>

void foliated_triangulations::debug_print_cells ( Container && t_cells )

Write to debug log timevalues of each vertex in the cell and the resulting cell->info.

Template Parameters

dimension	The dimensionality of the simplices
Container	The type of container

Parameters

t_cells The cells to write to debug log

Definition at line 667 of file Foliated_triangulation.hpp.

References foliated_triangulations::debug_print_cells().

Referenced by foliated_triangulations::debug_print_cells().

◆ expected_cell_type()

template<int dimension>

auto foliated_triangulations::expected_cell_type ( Cell_handle_t< dimension > const & t_cell )

Classifies cells by their timevalues.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_cell The simplex to check

Returns: The type of the simplex

Definition at line 503 of file Foliated_triangulation.hpp.

References foliated_triangulations::expected_cell_type().

Referenced by foliated_triangulations::expected_cell_type().

◆ expected_timevalue()

template<int dimension>

auto foliated_triangulations::expected_timevalue	(	Vertex_handle_t< dimension > const &	t_vertex,
		double	t_initial_radius,
		double	t_foliation_spacing
	)		-> Int_precision

Find the expected timevalue for a vertex.

The formula for the expected timevalue is:

\[t=\frac{R-I+S}{S}\]

Where R is radius, I is INITIAL_RADIUS, and S is RADIAL_SEPARATION

Template Parameters

dimension Dimensionality of the vertex

Parameters

t_vertex	The vertex
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: The effective radius of the vertex

Definition at line 309 of file Foliated_triangulation.hpp.

References foliated_triangulations::expected_timevalue().

Referenced by foliated_triangulations::expected_timevalue(), and foliated_triangulations::FoliatedTriangulation< 3 >::print_vertices().

◆ filter_cells()

template<int dimension>

auto foliated_triangulations::filter_cells	(	std::vector< Cell_handle_t< dimension > > const &	t_cells,
		Cell_type const &	t_cell_type
	)		-> std::vector<Cell_handle_t<dimension>>

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_cells	The container of simplices
t_cell_type	The type of simplex to filter by

Returns: A container of simplices filtered by type

Definition at line 269 of file Foliated_triangulation.hpp.

References foliated_triangulations::filter_cells().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::filter_cells().

◆ filter_edges()

template<int dimension>

auto foliated_triangulations::filter_edges	(	std::vector< Edge_handle_t< dimension > > const &	t_edges,
		bool	t_is_Timelike_pred
	)		-> std::vector<Edge_handle_t<dimension>>

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_edges	The container of edges to filter
t_is_Timelike_pred	The predicate to filter by

Returns: A container of is_Timelike edges

Definition at line 250 of file Foliated_triangulation.hpp.

References foliated_triangulations::filter_edges().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::filter_edges().

◆ find_bad_vertex()

template<int dimension>

auto foliated_triangulations::find_bad_vertex ( Cell_handle_t< dimension > const & cell ) -> Vertex_handle_t<dimension>

Find the vertex that is causing a cell's foliation to be invalid.

Template Parameters

dimension Dimensionality of the cell

Parameters

cell	The cell to check

Returns: The offending vertex

Definition at line 809 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_bad_vertex().

Referenced by foliated_triangulations::find_bad_vertex().

◆ find_cell()

template<int dimension>

auto foliated_triangulations::find_cell	(	Delaunay_t< dimension > const &	delaunay,
		Vertex_handle_t< dimension > const &	vh1,
		Vertex_handle_t< dimension > const &	vh2,
		Vertex_handle_t< dimension > const &	vh3,
		Vertex_handle_t< dimension > const &	vh4
	)		-> std::optional<Cell_handle_t<dimension>>

Returns the cell containing the vertices.

Template Parameters

dimension The dimensionality of the triangulation

Parameters

delaunay	The triangulation
vh1	The first vertex
vh2	The second vertex
vh3	The third vertex
vh4	The fourth vertex

Returns: The cell containing the vertices

See also: https://doc.cgal.org/latest/Triangulation_3/classCGAL_1_1Triangulation__3.html#a8766c9a0c2a84203be31537e5e015646

Definition at line 165 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_cell().

Referenced by foliated_triangulations::find_cell().

◆ find_incorrect_cells()

template<int dimension>

auto foliated_triangulations::find_incorrect_cells ( Delaunay_t< dimension > const & t_triangulation )

Check all finite cells in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: A container of cells that are not classified correctly

Definition at line 600 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_incorrect_cells().

Referenced by foliated_triangulations::find_incorrect_cells().

◆ find_incorrect_vertices() [1/2]

template<int dimension>

auto foliated_triangulations::find_incorrect_vertices	(	Delaunay_t< dimension > const &	t_triangulation,
		double	t_initial_radius,
		double	t_foliation_spacing
	)

Obtain vertices with incorrect timevalues.

Template Parameters

dimension Dimensionality of the vertices and Delaunay triangulation

Parameters

t_triangulation	The Delaunay triangulation
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: A container of vertices with incorrect timevalues

Definition at line 449 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_incorrect_vertices().

◆ find_incorrect_vertices() [2/2]

template<int dimension>

auto foliated_triangulations::find_incorrect_vertices	(	std::vector< Cell_handle_t< dimension > > const &	t_cells,
		double	t_initial_radius,
		double	t_foliation_spacing
	)

Obtain vertices with incorrect timevalues.

Template Parameters

dimension Dimensionality of vertices and cells

Parameters

t_cells	Container of cells to check
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: A container of vertices with incorrect timevalues

Definition at line 425 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_incorrect_vertices().

Referenced by foliated_triangulations::find_incorrect_vertices().

◆ find_max_timevalue()

template<int dimension, ContainerType Container>

auto foliated_triangulations::find_max_timevalue ( Container && t_vertices ) -> Int_precision

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_vertices The container of vertices

Returns: The maximum timevalue in the container

Definition at line 192 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_max_timevalue().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::find_max_timevalue().

◆ find_min_timevalue()

template<int dimension, ContainerType Container>

auto foliated_triangulations::find_min_timevalue ( Container && t_vertices ) -> Int_precision

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_vertices The container of vertices

Returns: The minimum timevalue in the container

Definition at line 210 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_min_timevalue().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::find_min_timevalue().

◆ find_vertex()

template<int dimension>

auto foliated_triangulations::find_vertex	(	Delaunay_t< dimension > const &	delaunay,
		Point_t< dimension > const &	point
	)		-> std::optional<Vertex_handle_t<dimension>>

Returns the vertex containing the given point.

Template Parameters

dimension The dimensionality of the triangulation

Parameters

delaunay	The triangulation
point	The point to find the vertex for

Returns: The vertex containing the given point

See also: https://doc.cgal.org/latest/Triangulation_3/classCGAL_1_1Triangulation__3.html#a5b45572c663e5d2c10f26e7be421e140

Definition at line 142 of file Foliated_triangulation.hpp.

References foliated_triangulations::find_vertex().

Referenced by foliated_triangulations::find_vertex().

◆ fix_cells()

template<int dimension>

auto foliated_triangulations::fix_cells ( Delaunay_t< dimension > const & t_triangulation ) -> bool

Fix simplices with the wrong type.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_triangulation The Delaunay triangulation

Returns: True if cells->info() was fixed

Definition at line 618 of file Foliated_triangulation.hpp.

References foliated_triangulations::fix_cells().

Referenced by foliated_triangulations::fix_cells().

◆ fix_timevalues()

template<int dimension>

auto foliated_triangulations::fix_timevalues ( Delaunay_t< dimension > & t_triangulation ) -> bool

Fix the vertices of a cell to be consistent with the foliation.

Template Parameters

dimension Dimensionality of the triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: True if incorrectly foliated simplices were fixed

Definition at line 843 of file Foliated_triangulation.hpp.

References foliated_triangulations::fix_timevalues().

Referenced by foliated_triangulations::fix_timevalues().

◆ fix_vertices() [1/2]

template<int dimension>

auto foliated_triangulations::fix_vertices	(	Delaunay_t< dimension > const &	t_triangulation,
		double const	t_initial_radius,
		double const	t_foliation_spacing
	)		-> bool

Fix vertices with incorrect timevalues.

Changes vertex->info() to the correct timevalue

Template Parameters

dimension Dimensionality of the vertices and Delaunay triangulation

Parameters

t_triangulation	The triangulation
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: True if any vertex->info() was fixed

Definition at line 490 of file Foliated_triangulation.hpp.

References foliated_triangulations::fix_vertices().

◆ fix_vertices() [2/2]

template<int dimension>

auto foliated_triangulations::fix_vertices	(	std::vector< Cell_handle_t< dimension > > const &	t_cells,
		double	t_initial_radius,
		double	t_foliation_spacing
	)

Fix vertices with incorrect timevalues.

Changes vertex->info() to the correct timevalue using foliated_triangulations::expected_timevalue

Template Parameters

dimension Dimensionality of vertices and cells

Parameters

t_cells	Container of cells to check
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing

Returns: True if any vertex->info() was fixed

Definition at line 467 of file Foliated_triangulation.hpp.

References foliated_triangulations::fix_vertices().

Referenced by foliated_triangulations::fix_vertices().

◆ get_vertices_from_cells()

template<int dimension>

auto foliated_triangulations::get_vertices_from_cells ( std::vector< Cell_handle_t< dimension > > const & t_cells )

Extracts vertices from cells.

Parameters

t_cells The cells from which to extract vertices

Returns: All of the vertices contained in the cells

Definition at line 402 of file Foliated_triangulation.hpp.

References foliated_triangulations::get_vertices_from_cells().

Referenced by foliated_triangulations::get_vertices_from_cells().

◆ is_cell_type_correct()

template<int dimension>

auto foliated_triangulations::is_cell_type_correct ( Cell_handle_t< dimension > const & t_cell ) -> bool

Checks if a cell is classified correctly.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_cell The simplex to check

Returns: True if the cell_info matches expected cell_info

Definition at line 569 of file Foliated_triangulation.hpp.

References foliated_triangulations::is_cell_type_correct().

Referenced by foliated_triangulations::is_cell_type_correct().

◆ is_vertex_timevalue_correct()

template<int dimension>

auto foliated_triangulations::is_vertex_timevalue_correct	(	Vertex_handle_t< dimension > const &	t_vertex,
		double const	t_initial_radius,
		double const	t_foliation_spacing
	)		-> bool

Checks if vertex timevalue is correct.

Template Parameters

dimension Dimensionality of the vertex

Parameters

t_vertex	The vertex
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: True if the timevalue of the vertex matches its effective radius

Definition at line 326 of file Foliated_triangulation.hpp.

References foliated_triangulations::is_vertex_timevalue_correct().

Referenced by foliated_triangulations::is_vertex_timevalue_correct().

◆ make_causal_vertices()

template<int dimension>

auto foliated_triangulations::make_causal_vertices	(	std::span< Point_t< dimension > const >	vertices,
		std::span< size_t const >	timevalues
	)		-> Causal_vertices_t<dimension>

Create causal vertices from vertices and timevalues.

Template Parameters

dimension Dimensionality of the manifold

Parameters

vertices	The vertices of the manifold
timevalues	The timevalue of each vertex

Returns: A container of vertices that have an associated timevalue

Definition at line 89 of file Foliated_triangulation.hpp.

References foliated_triangulations::make_causal_vertices().

Referenced by foliated_triangulations::make_causal_vertices().

◆ make_foliated_ball()

template<int dimension>

auto foliated_triangulations::make_foliated_ball	(	Int_precision const	t_simplices,
		Int_precision const	t_timeslices,
		double const	initial_radius = `INITIAL_RADIUS`,
		double const	foliation_spacing = `FOLIATION_SPACING`
	)

Make foliated ball.

Makes a solid ball of successive layers of spheres at a given radius.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_simplices	The desired number of simplices in the triangulation
t_timeslices	The desired number of timeslices in the triangulation
initial_radius	The radius of the first time slice
foliation_spacing	The distance between successive time slices

Returns: A container of (vertex, timevalue) pairs

Definition at line 882 of file Foliated_triangulation.hpp.

References foliated_triangulations::make_foliated_ball().

Referenced by foliated_triangulations::make_foliated_ball().

◆ make_triangulation()

template<int dimension>

auto foliated_triangulations::make_triangulation	(	Int_precision const	t_simplices,
		Int_precision	t_timeslices,
		double const	initial_radius = `INITIAL_RADIUS`,
		double const	foliation_spacing = `FOLIATION_SPACING`
	)		-> Delaunay_t<dimension>

Make a Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_simplices	Number of desired simplices
t_timeslices	Number of desired timeslices
initial_radius	Radius of first timeslice
foliation_spacing	Radial separation between timeslices

Returns: A Delaunay triangulation with a timevalue for each vertex

Definition at line 916 of file Foliated_triangulation.hpp.

References foliated_triangulations::make_triangulation().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::make_triangulation().

◆ print_cell()

template<int dimension>

void foliated_triangulations::print_cell ( Cell_handle_t< dimension > cell )

Print a cell in the triangulation.

Template Parameters

dimension The dimensionality of the triangulation

Parameters

cell	The cell to print

Definition at line 634 of file Foliated_triangulation.hpp.

References foliated_triangulations::print_cell().

Referenced by foliated_triangulations::print_cell().

◆ print_cells()

template<int dimension, typename Container >

void foliated_triangulations::print_cells ( Container && t_cells )

Print timevalues of each vertex in the cell and the resulting cell->info()

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_cells The cells to print

Definition at line 652 of file Foliated_triangulation.hpp.

References foliated_triangulations::print_cells().

Referenced by foliated_triangulations::print_cells().

◆ print_edge()

template<int dimension>

void foliated_triangulations::print_edge ( Edge_handle_t< dimension > const & t_edge )

Print edge.

An edge is represented by a cell and two indices which refer to the vertices of the cell connected by the edge. The data is stored in a CGAL::Triple, which is an extension of std::pair.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_edge The edge to print

See also: https://doc.cgal.org/latest/TDS_3/index.html#fig__TDS3figrepres; https://doc.cgal.org/latest/STL_Extension/classCGAL_1_1Triple.html

Definition at line 705 of file Foliated_triangulation.hpp.

References foliated_triangulations::print_edge().

Referenced by foliated_triangulations::print_edge().

◆ print_neighboring_cells()

template<int dimension>

void foliated_triangulations::print_neighboring_cells ( Cell_handle_t< dimension > cell )

Print neighboring cells.

Template Parameters

dimension The dimensionality of the simplices

Parameters

cell	The cell to print neighbors of

Definition at line 687 of file Foliated_triangulation.hpp.

References foliated_triangulations::print_neighboring_cells().

Referenced by foliated_triangulations::print_neighboring_cells().

◆ squared_radius()

template<int dimension>

auto foliated_triangulations::squared_radius ( Vertex_handle_t< dimension > const & t_vertex ) -> double

Calculate the squared radius from the origin.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_vertex The vertex to check

Returns: The squared radial distance of the vertex from the origin

Definition at line 289 of file Foliated_triangulation.hpp.

References foliated_triangulations::squared_radius().

Referenced by foliated_triangulations::squared_radius().

◆ volume_per_timeslice()

template<int dimension, ContainerType Container>

auto foliated_triangulations::volume_per_timeslice ( Container && t_facets ) -> std::multimap<Int_precision, Facet_t<3>>

Collect spacelike facets into a container indexed by time value.

Warning! Turning on debugging info will generate gigabytes of logs.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_facets A container of facets

Returns: Container with spacelike facets per timeslice

Definition at line 724 of file Foliated_triangulation.hpp.

References foliated_triangulations::volume_per_timeslice().

Referenced by foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), and foliated_triangulations::volume_per_timeslice().

Variable Documentation

◆ compare_v_info

template<int dimension>

auto constexpr foliated_triangulations::compare_v_info

constexpr

Initial value:

= [](Vertex_handle_t<dimension> const& lhs,
                                     Vertex_handle_t<dimension> const& rhs) {
    return lhs->info() < rhs->info();
  }

Template Parameters

dimension The dimensionality of the simplices

Returns: True if timevalue of lhs is less than rhs

Definition at line 183 of file Foliated_triangulation.hpp.

◆ MAX_FIX_PASSES

int constexpr foliated_triangulations::MAX_FIX_PASSES = 50

staticconstexpr

Definition at line 81 of file Foliated_triangulation.hpp.

Classes

Concepts

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ Causal_vertices_t

◆ Cell_handle_t

◆ Delaunay_t

◆ Edge_handle_t

◆ Face_handle_t

◆ Facet_t

◆ FoliatedTriangulation_3

◆ FoliatedTriangulation_4

◆ Point_t

◆ Spherical_points_generator_t

◆ Vertex_handle_t

Enumeration Type Documentation

◆ Cell_type

Function Documentation

◆ check_cells()

◆ check_timevalues()

◆ check_vertices()

◆ classify_edge()

◆ collect_cells()

◆ collect_edges()

◆ collect_vertices()

◆ debug_print_cells()

◆ expected_cell_type()

◆ expected_timevalue()

◆ filter_cells()

◆ filter_edges()

◆ find_bad_vertex()

◆ find_cell()

◆ find_incorrect_cells()

◆ find_incorrect_vertices() [1/2]

◆ find_incorrect_vertices() [2/2]

◆ find_max_timevalue()

◆ find_min_timevalue()

◆ find_vertex()

◆ fix_cells()

◆ fix_timevalues()

◆ fix_vertices() [1/2]

◆ fix_vertices() [2/2]

◆ get_vertices_from_cells()

◆ is_cell_type_correct()

◆ is_vertex_timevalue_correct()

◆ make_causal_vertices()

◆ make_foliated_ball()

◆ make_triangulation()

◆ print_cell()

◆ print_cells()

◆ print_edge()

◆ print_neighboring_cells()

◆ squared_radius()

◆ volume_per_timeslice()

Variable Documentation

◆ compare_v_info

◆ MAX_FIX_PASSES