Supported construction, inspection, classification, and repair operations for foliated Delaunay triangulations. More...

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

Typedefs
using	FoliatedTriangulation_3 = FoliatedTriangulation<3>
	Three-dimensional foliated Delaunay triangulation.

Functions
template<int dimension>
auto	check_cells (Delaunay_t< dimension > const &t_triangulation) -> bool
	Check all finite cells in the Delaunay triangulation.
template<int dimension>
auto	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	classify_edge (Edge_handle_t< dimension > const &t_edge) -> EdgeType
	Predicate to classify edge as timelike or spacelike.
template<int dimension>
auto	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	collect_edges (Delaunay_t< dimension > const &delaunay)
	Returns a container of all the finite edges in the triangulation.
template<int dimension, detail::ConstForwardRange Container>
auto	collect_spacelike_facets (Container const &t_facets) -> std::vector< std::pair< Int_precision, Facet_t< dimension > > >
	Collect spacelike facets into a contiguous container ordered by time value.
template<int dimension>
auto	collect_vertices (Delaunay_t< dimension > const &t_triangulation)
	Obtain all finite vertices in the Delaunay triangulation.
template<int dimension, detail::ConstForwardRange Container>
void	debug_print_cells (Container const &t_cells)
	Write to debug log timevalues of each vertex in the cell and the resulting cell->info.
template<int dimension>
auto	expected_cell_type (Cell_handle_t< dimension > const &t_cell)
	Classifies cells by their timevalues.
template<int dimension>
auto	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	filter_cells (std::vector< Cell_handle_t< dimension > > const &t_cells, CellType const &t_cell_type) -> std::vector< Cell_handle_t< dimension > >
template<int dimension>
auto	filter_edges (std::vector< Edge_handle_t< dimension > > const &t_edges, EdgeType const edge_type) -> std::vector< Edge_handle_t< dimension > >
template<int dimension>
auto	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	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	find_incorrect_cells (Delaunay_t< dimension > const &t_triangulation)
	Check all finite cells in the Delaunay triangulation.
template<int dimension>
auto	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	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>
auto	find_invalid_timevalue_cells (Delaunay_t< dimension > const &t_triangulation) -> std::vector< Cell_handle_t< dimension > >
	Find cells whose vertex timevalues violate foliation.
template<int dimension, detail::ConstForwardRange Container>
auto	find_max_timevalue (Container const &t_vertices) -> Int_precision
template<int dimension, detail::ConstForwardRange Container>
auto	find_min_timevalue (Container const &t_vertices) -> Int_precision
template<int dimension>
auto	find_vertex (Delaunay_t< dimension > const &delaunay, Point_t< dimension > const &point) -> std::optional< Vertex_handle_t< dimension > >
	Find the vertex whose stored point equals the requested point.
template<int dimension>
auto	fix_cells (Delaunay_t< dimension > &t_triangulation) -> bool
	Fix simplices with the wrong type.
template<int dimension>
auto	fix_timevalues (Delaunay_t< dimension > &t_triangulation) -> bool
	Fix the vertices of a cell to be consistent with the foliation.
template<int dimension>
auto	fix_vertices (Delaunay_t< dimension > &t_triangulation, double const t_initial_radius, double const t_foliation_spacing) -> bool
	Fix vertices with incorrect timevalues.
template<int dimension>
auto	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	get_vertices_from_cells (std::vector< Cell_handle_t< dimension > > const &t_cells)
	Extracts vertices from cells.
template<int dimension>
auto	has_valid_timevalues (Delaunay_t< dimension > const &triangulation) -> bool
	Check whether all cell timevalues form a valid foliation.
template<int dimension>
auto	is_cell_type_correct (Cell_handle_t< dimension > const &t_cell) -> bool
	Checks if a cell is classified correctly.
template<int dimension>
auto	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	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, std::uniform_random_bit_generator Generator>
auto	make_foliated_ball (Int_precision const t_simplices, Int_precision const t_timeslices, double const initial_radius, double const foliation_spacing, Generator &generator)
	Make foliated ball.
template<int dimension, std::uniform_random_bit_generator Generator>
auto	make_triangulation (Int_precision const t_simplices, Int_precision t_timeslices, double const initial_radius, double const foliation_spacing, Generator &generator) -> Delaunay_t< dimension >
	Make a Delaunay triangulation.
template<int dimension>
void	print_cell (Cell_handle_t< dimension > cell)
	Print a cell in the triangulation.
template<int dimension, detail::ConstForwardRange Container>
void	print_cells (Container const &t_cells)
	Print timevalues of each vertex in the cell and the resulting cell->info().
template<int dimension>
void	print_edge (Edge_handle_t< dimension > const &t_edge)
	Print edge.
template<int dimension>
void	print_neighboring_cells (Cell_handle_t< dimension > cell)
	Print neighboring cells.
template<int dimension>
auto	squared_radius (Vertex_handle_t< dimension > const &t_vertex) -> double
	Calculate the squared radius from the origin.
template<int dimension, detail::ConstForwardRange Container>
auto	volume_per_timeslice (Container const &t_facets) -> std::multimap< Int_precision, Facet_t< dimension > >
	Collect spacelike facets into a container indexed by time value.

Variables
template<int dimension>
constexpr auto	compare_v_info

Detailed Description

Supported construction, inspection, classification, and repair operations for foliated Delaunay triangulations.

CGAL handles and descriptors returned by these operations borrow from the triangulation named by the function. All handles supplied to one operation must be valid and belong to that same triangulation. Copying a triangulation does not transfer handle provenance, and topology mutation may invalidate outstanding handles, iterators, circulators, and descriptors.

See also: Multithreaded CGAL contract

Typedef Documentation

◆ FoliatedTriangulation_3

using cdt::foliated_triangulations::FoliatedTriangulation_3 = FoliatedTriangulation<3>

Three-dimensional foliated Delaunay triangulation.

Definition at line 2068 of file Foliated_triangulation.hpp.

Function Documentation

◆ check_cells()

template<int dimension>

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

nodiscard

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 890 of file Foliated_triangulation.hpp.

Referenced by cdt::foliated_triangulations::FoliatedTriangulation< 3 >::check_all_cells().

◆ check_vertices()

template<int dimension>

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

nodiscard

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 676 of file Foliated_triangulation.hpp.

Referenced by cdt::foliated_triangulations::FoliatedTriangulation< 3 >::check_all_vertices().

◆ classify_edge()

template<int dimension>

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

nodiscard

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: The causal edge classification

Definition at line 534 of file Foliated_triangulation.hpp.

References CDT_PRETTY_FUNCTION, cdt::SPACELIKE, and cdt::TIMELIKE.

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

◆ collect_cells()

template<int dimension>

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

nodiscard

Obtain all finite cells in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The triangulation

Returns: Borrowed finite-cell handles tied to t_triangulation and subject to its mutation-invalidation rules.

Definition at line 693 of file Foliated_triangulation.hpp.

Referenced by cdt::ergodic_moves::do_23_move(), find_incorrect_cells(), find_incorrect_vertices(), find_invalid_timevalue_cells(), fix_vertices(), and cdt::ergodic_moves::propose_23_move().

◆ collect_edges()

template<int dimension>

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

nodiscard

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: Borrowed finite-edge descriptors tied to delaunay and subject to its mutation-invalidation rules.

Definition at line 422 of file Foliated_triangulation.hpp.

Referenced by cdt::ergodic_moves::do_32_move(), cdt::ergodic_moves::do_44_move(), cdt::ergodic_moves::propose_32_move(), and cdt::ergodic_moves::propose_44_move().

◆ collect_spacelike_facets()

template<int dimension, detail::ConstForwardRange Container>

auto cdt::foliated_triangulations::collect_spacelike_facets ( Container const & t_facets ) -> std::vector< std::pair< Int_precision, Facet_t< dimension > > >

nodiscard

Collect spacelike facets into a contiguous container ordered by time value.

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

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_facets Facets whose cell handles are valid and belong to one triangulation.

Returns: Contiguous container with spacelike facets per timeslice. The facet descriptors borrow from the source triangulation and follow its mutation-invalidation rules.

Definition at line 1027 of file Foliated_triangulation.hpp.

References CDT_PRETTY_FUNCTION.

Referenced by volume_per_timeslice().

◆ collect_vertices()

template<int dimension>

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

nodiscard

Obtain all finite vertices in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: Borrowed finite-vertex handles tied to t_triangulation and subject to its mutation-invalidation rules.

Definition at line 655 of file Foliated_triangulation.hpp.

Referenced by cdt::ergodic_moves::do_62_move(), and cdt::ergodic_moves::propose_62_move().

◆ debug_print_cells()

template<int dimension, detail::ConstForwardRange Container>

void cdt::foliated_triangulations::debug_print_cells ( Container const & 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 968 of file Foliated_triangulation.hpp.

Referenced by find_bad_vertex().

◆ expected_cell_type()

template<int dimension>

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

nodiscard

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 815 of file Foliated_triangulation.hpp.

References cdt::ACAUSAL, CDT_PRETTY_FUNCTION, cdt::ONE_THREE, cdt::THREE_ONE, cdt::TWO_TWO, and cdt::UNCLASSIFIED.

Referenced by cdt::ergodic_moves::detail::execute(), cdt::ergodic_moves::detail::execute(), cdt::ergodic_moves::detail::find_adjacent_31_cell(), cdt::ergodic_moves::detail::find_bistellar_flip_location(), cdt::ergodic_moves::detail::is_32_movable(), cdt::ergodic_moves::detail::is_62_movable(), is_cell_type_correct(), and cdt::ergodic_moves::detail::prepare_two_three().

◆ expected_timevalue()

template<int dimension>

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

nodiscard

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 the initial radius, and S is the foliation spacing.

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

Precondition: t_vertex is a valid handle and both geometric parameters are finite, with t_foliation_spacing greater than zero.

Returns: The timeslice label implied by the vertex radius.

Definition at line 617 of file Foliated_triangulation.hpp.

References squared_radius().

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

◆ filter_cells()

template<int dimension>

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

nodiscard

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 575 of file Foliated_triangulation.hpp.

Referenced by cdt::ergodic_moves::do_23_move(), and cdt::ergodic_moves::propose_23_move().

◆ filter_edges()

template<int dimension>

auto cdt::foliated_triangulations::filter_edges	(	std::vector< Edge_handle_t< dimension > > const &	t_edges,
		EdgeType const	edge_type ) -> std::vector< Edge_handle_t< dimension > >

nodiscard

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_edges	The container of edges to filter
edge_type	The edge classification to retain

Returns: A container of edges with the requested classification

Definition at line 557 of file Foliated_triangulation.hpp.

References classify_edge().

Referenced by cdt::ergodic_moves::do_32_move(), cdt::ergodic_moves::do_44_move(), cdt::ergodic_moves::propose_32_move(), and cdt::ergodic_moves::propose_44_move().

◆ find_bad_vertex()

template<int dimension>

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

nodiscard

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

Template Parameters

dimension Dimensionality of the cell

Parameters

cell	Valid cell handle from the triangulation being repaired.

Returns: A borrowed handle to the offending vertex in cell, with the same source-triangulation lifetime and invalidation rules.

Definition at line 1146 of file Foliated_triangulation.hpp.

References CDT_PRETTY_FUNCTION, and debug_print_cells().

Referenced by fix_timevalues().

◆ find_cell()

template<int dimension>

auto cdt::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 > >

nodiscard

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

Precondition: All four handles are valid and belong to delaunay.

Returns: A cell handle borrowing from delaunay, or std::nullopt when those vertices do not form a cell. The returned handle is subject to the triangulation's mutation-invalidation rules.

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

Definition at line 472 of file Foliated_triangulation.hpp.

◆ find_incorrect_cells()

template<int dimension>

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

nodiscard

Check all finite cells in the Delaunay triangulation.

Template Parameters

dimension Dimensionality of the Delaunay triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: Borrowed handles for incorrectly classified cells, tied to t_triangulation and subject to its mutation-invalidation rules.

Definition at line 904 of file Foliated_triangulation.hpp.

References collect_cells().

Referenced by fix_cells().

◆ find_incorrect_vertices() [1/2]

template<int dimension>

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

nodiscard

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: Borrowed handles for vertices with incorrect timevalues, tied to t_triangulation and subject to its mutation-invalidation rules.

Definition at line 760 of file Foliated_triangulation.hpp.

References collect_cells(), and find_incorrect_vertices().

◆ find_incorrect_vertices() [2/2]

template<int dimension>

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

nodiscard

Obtain vertices with incorrect timevalues.

Template Parameters

dimension Dimensionality of vertices and cells

Parameters

t_cells	Valid cells that all belong to one triangulation.
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	The spacing between successive leaves

Returns: Borrowed handles for vertices with incorrect timevalues, retaining the source triangulation's lifetime and invalidation rules.

Definition at line 735 of file Foliated_triangulation.hpp.

References get_vertices_from_cells().

Referenced by find_incorrect_vertices(), and fix_vertices().

◆ find_invalid_timevalue_cells()

template<int dimension>

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

nodiscard

Find cells whose vertex timevalues violate 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: Borrowed handles for invalid cells, tied to t_triangulation and subject to its mutation-invalidation rules; empty means the foliation is valid.

Definition at line 1115 of file Foliated_triangulation.hpp.

References collect_cells().

Referenced by fix_timevalues(), and has_valid_timevalues().

◆ find_max_timevalue()

template<int dimension, detail::ConstForwardRange Container>

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

nodiscard

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_vertices The container of vertices

Returns: The maximum timevalue in the container

Exceptions

std::invalid_argument If t_vertices is empty.

Definition at line 500 of file Foliated_triangulation.hpp.

References compare_v_info.

◆ find_min_timevalue()

template<int dimension, detail::ConstForwardRange Container>

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

nodiscard

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_vertices The container of vertices

Returns: The minimum timevalue in the container

Exceptions

std::invalid_argument If t_vertices is empty.

Definition at line 517 of file Foliated_triangulation.hpp.

References compare_v_info.

◆ find_vertex()

template<int dimension>

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

nodiscard

Find the vertex whose stored point equals the requested point.

Template Parameters

dimension The dimensionality of the triangulation

Parameters

delaunay	The triangulation
point	The point to find the vertex for

Returns: A handle borrowing from delaunay, or std::nullopt when no vertex stores point. The handle is subject to the triangulation's mutation-invalidation rules.

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

Definition at line 446 of file Foliated_triangulation.hpp.

Referenced by cdt::ergodic_moves::detail::execute().

◆ fix_cells()

template<int dimension>

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

nodiscard

Fix simplices with the wrong type.

Only cell metadata is changed; the triangulation topology and its handles are not replaced by this operation.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_triangulation The Delaunay triangulation

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

Definition at line 924 of file Foliated_triangulation.hpp.

References find_incorrect_cells().

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

◆ fix_timevalues()

template<int dimension>

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

nodiscard

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

Removes selected vertices from the triangulation. A successful repair changes its topology and may invalidate any outstanding handles, iterators, circulators, and facet or edge descriptors.

Template Parameters

dimension Dimensionality of the triangulation

Parameters

t_triangulation The Delaunay triangulation

Returns: True if incorrectly foliated simplices were fixed

Definition at line 1182 of file Foliated_triangulation.hpp.

References find_bad_vertex(), and find_invalid_timevalue_cells().

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

◆ fix_vertices() [1/2]

template<int dimension>

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

nodiscard

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 802 of file Foliated_triangulation.hpp.

References collect_cells(), and fix_vertices().

◆ fix_vertices() [2/2]

template<int dimension>

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

nodiscard

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	Valid cells that all belong to one triangulation.
t_initial_radius	The initial radius of the radial foliation
t_foliation_spacing	Positive finite spacing between successive leaves.

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

Definition at line 779 of file Foliated_triangulation.hpp.

References find_incorrect_vertices().

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

◆ get_vertices_from_cells()

template<int dimension>

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

nodiscard

Extracts vertices from cells.

Parameters

t_cells Valid cells that all belong to one triangulation.

Returns: Borrowed handles for all vertices contained in t_cells. They retain the cells' source-triangulation lifetime and invalidation rules.

Definition at line 711 of file Foliated_triangulation.hpp.

Referenced by find_incorrect_vertices().

◆ has_valid_timevalues()

template<int dimension>

auto cdt::foliated_triangulations::has_valid_timevalues ( Delaunay_t< dimension > const & triangulation ) -> bool

nodiscard

Check whether all cell timevalues form a valid foliation.

Template Parameters

dimension Compile-time triangulation dimension.

Parameters

triangulation Triangulation whose finite cells are classified.

Returns: Whether every finite cell has a supported causal classification.

Definition at line 1136 of file Foliated_triangulation.hpp.

References find_invalid_timevalue_cells().

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

◆ is_cell_type_correct()

template<int dimension>

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

nodiscard

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 875 of file Foliated_triangulation.hpp.

References cdt::ACAUSAL, expected_cell_type(), and cdt::UNCLASSIFIED.

Referenced by cdt::ergodic_moves::detail::find_adjacent_31_cell(), cdt::ergodic_moves::detail::find_bistellar_flip_location(), cdt::ergodic_moves::detail::is_32_movable(), cdt::ergodic_moves::detail::is_62_movable(), and cdt::ergodic_moves::detail::prepare_two_three().

◆ is_vertex_timevalue_correct()

template<int dimension>

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

nodiscard

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 635 of file Foliated_triangulation.hpp.

References expected_timevalue().

◆ make_causal_vertices()

template<int dimension>

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

nodiscard

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

Exceptions

std::length_error	If the spans have different lengths.
std::out_of_range	If a timevalue cannot be represented by Int_precision.

Definition at line 392 of file Foliated_triangulation.hpp.

Referenced by cdt::manifolds::make_causal_vertices().

◆ make_foliated_ball()

template<int dimension, std::uniform_random_bit_generator Generator>

auto cdt::foliated_triangulations::make_foliated_ball	(	Int_precision const	t_simplices,
		Int_precision const	t_timeslices,
		double const	initial_radius,
		double const	foliation_spacing,
		Generator &	generator )

nodiscard

Make foliated ball.

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

Template Parameters

dimension	The dimensionality of the simplices
Generator	Uniform random bit generator type owned by the caller

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
generator	Caller-owned random stream whose state is maintained by the caller and advanced during this call

Returns: A container of (vertex, timevalue) pairs

Exceptions

std::invalid_argument	If a count is less than two, a radius or spacing is non-finite or nonpositive, or the parameters cannot populate a triangulation.
std::out_of_range	If a layer population cannot be represented by Int_precision.

Note: Once sampling begins, an exception does not roll back generator.

Definition at line 1231 of file Foliated_triangulation.hpp.

Referenced by make_triangulation().

◆ make_triangulation()

template<int dimension, std::uniform_random_bit_generator Generator>

auto cdt::foliated_triangulations::make_triangulation	(	Int_precision const	t_simplices,
		Int_precision	t_timeslices,
		double const	initial_radius,
		double const	foliation_spacing,
		Generator &	generator ) -> Delaunay_t< dimension >

nodiscard

Make a Delaunay triangulation.

Template Parameters

dimension	Dimensionality of the Delaunay triangulation
Generator	Uniform random bit generator type owned by the caller

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
generator	Caller-owned random stream whose state is maintained by the caller and advanced during this call

Returns: An owning Delaunay triangulation detached from the internal lock grid

Construction uses the configured parallel range operations when available. The returned triangulation does not borrow the temporary lock grid and can safely outlive this call. Its subsequent range operations are sequential; in a TBB-enabled build, callers can attach a compatible lock grid that they own to re-enable parallel execution.

Exceptions

std::invalid_argument	If the generation parameters are invalid or the generated point set cannot form a nonempty unique triangulation.
std::out_of_range	If a generated layer population cannot be represented by Int_precision.

Note: Once sampling begins, an exception does not roll back generator.

See also: CGAL triangulations

Definition at line 1329 of file Foliated_triangulation.hpp.

References CDT_PRETTY_FUNCTION, fix_cells(), fix_timevalues(), fix_vertices(), has_valid_timevalues(), and make_foliated_ball().

Referenced by cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation().

◆ print_cell()

template<int dimension>

void cdt::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 939 of file Foliated_triangulation.hpp.

Referenced by print_cells(), and print_neighboring_cells().

◆ print_cells()

template<int dimension, detail::ConstForwardRange Container>

void cdt::foliated_triangulations::print_cells ( Container const & 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 957 of file Foliated_triangulation.hpp.

References print_cell().

Referenced by cdt::foliated_triangulations::FoliatedTriangulation< 3 >::print_cells().

◆ print_edge()

template<int dimension>

void cdt::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 public type is the triangulation's canonical Delaunay::Edge alias.

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

Definition at line 1004 of file Foliated_triangulation.hpp.

◆ print_neighboring_cells()

template<int dimension>

void cdt::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 987 of file Foliated_triangulation.hpp.

References print_cell().

◆ squared_radius()

template<int dimension>

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

nodiscard

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 593 of file Foliated_triangulation.hpp.

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

◆ volume_per_timeslice()

template<int dimension, detail::ConstForwardRange Container>

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

nodiscard

Collect spacelike facets into a container indexed by time value.

Template Parameters

dimension The dimensionality of the simplices

Parameters

t_facets Facets whose cell handles are valid and belong to one triangulation.

Returns: Container with spacelike facets per timeslice. The facet descriptors borrow from the source triangulation and follow its mutation-invalidation rules.

Definition at line 1090 of file Foliated_triangulation.hpp.

References collect_spacelike_facets().

Variable Documentation

◆ compare_v_info

template<int dimension>

auto cdt::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 490 of file Foliated_triangulation.hpp.

Referenced by find_max_timevalue(), and find_min_timevalue().

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ FoliatedTriangulation_3

Function Documentation

◆ check_cells()

◆ check_vertices()

◆ classify_edge()

◆ collect_cells()

◆ collect_edges()

◆ collect_spacelike_facets()

◆ 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_invalid_timevalue_cells()

◆ find_max_timevalue()

◆ find_min_timevalue()

◆ find_vertex()

◆ fix_cells()

◆ fix_timevalues()

◆ fix_vertices() [1/2]

◆ fix_vertices() [2/2]

◆ get_vertices_from_cells()

◆ has_valid_timevalues()

◆ 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