Pachner moves on 2+1 dimensional foliated Delaunay triangulations. More...

#include <algorithm>
#include <array>
#include <bit>
#include <concepts>
#include <cstddef>
#include <expected>
#include <limits>
#include <optional>
#include <random>
#include <ranges>
#include <string>
#include <unordered_set>
#include <utility>
#include <vector>
#include "Manifold.hpp"
#include "Move_outcome.hpp"
#include "Move_tracker.hpp"

Include dependency graph for Ergodic_moves_3.hpp:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Namespaces
namespace	cdt
	clang-15 does not support std::format

Typedefs
using	cdt::ergodic_moves::Cell_container = std::vector<Cell_handle>
	Collection of three-dimensional cell handles.
using	cdt::ergodic_moves::Cell_handle = Cell_handle_t<3>
	Three-dimensional CGAL cell handle.
using	cdt::ergodic_moves::detail::Cell_points = std::array<Point_t<3>, 4>
using	cdt::ergodic_moves::Delaunay = Delaunay_t<3>
	Three-dimensional Delaunay triangulation used by move implementations.
using	cdt::ergodic_moves::Edge_container = std::vector<Edge_handle>
	Collection of three-dimensional edge descriptors.
using	cdt::ergodic_moves::Edge_handle = Edge_handle_t<3>
	Three-dimensional CGAL edge descriptor.
using	cdt::ergodic_moves::detail::Edge_points = std::array<Point_t<3>, 2>
using	cdt::ergodic_moves::detail::Execution = std::expected<void, MoveError>
using	cdt::ergodic_moves::Expected = MoveResult<Manifold>
	Fallible manifold transformation returned by public move functions.
using	cdt::ergodic_moves::Manifold = manifolds::Manifold_3
	Three-dimensional spherical CDT manifold operated on by this move set.
using	cdt::ergodic_moves::Vertex_container = std::vector<Vertex_handle>
	Collection of three-dimensional vertex handles.
using	cdt::ergodic_moves::Vertex_handle = Vertex_handle_t<3>
	Three-dimensional CGAL vertex handle.

Functions
auto	cdt::ergodic_moves::detail::accept_post_mutation (Delaunay const &triangulation) noexcept -> bool
	Default validator for internal post-mutation test seams.
auto	cdt::ergodic_moves::detail::bistellar_flip (Delaunay const &source_triangulation, Edge_handle source_edge, Vertex_handle source_top, Vertex_handle source_bottom) -> std::optional< Delaunay >
	Perform a bistellar flip on triangulation via the given edge.
template<typename Post_mutation_validator>
auto	cdt::ergodic_moves::detail::bistellar_flip_impl (Delaunay const &source_triangulation, Edge_handle const source_edge, Vertex_handle const source_top, Vertex_handle const source_bottom, Post_mutation_validator post_mutation_validator) -> std::optional< Delaunay >
auto	cdt::ergodic_moves::detail::canonical_cell_points (Cell_handle const &cell) -> std::array< Point_t< 3 >, 4 >
auto	cdt::ergodic_moves::detail::canonical_edge_descriptor (Delaunay const &triangulation, Edge_handle const &edge) -> std::optional< Edge_handle >
	Rebind an edge to its canonical finite incident cell.
auto	cdt::ergodic_moves::detail::canonical_edge_points (Edge_handle const &edge) -> std::array< Point_t< 3 >, 2 >
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::detail::canonical_random_element (Cell_container &cells, Generator &generator) -> std::optional< Cell_handle >
template<typename Container, std::uniform_random_bit_generator Generator, typename Comparator>
auto	cdt::ergodic_moves::detail::canonical_random_element (Container &candidates, Generator &generator, Comparator comparator) -> std::optional< typename Container::value_type >
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::detail::canonical_random_element (Edge_container &edges, Generator &generator) -> std::optional< Edge_handle >
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::detail::canonical_random_element (Vertex_container &vertices, Generator &generator) -> std::optional< Vertex_handle >
void	cdt::ergodic_moves::detail::canonicalize (Cell_container &cells)
void	cdt::ergodic_moves::detail::canonicalize (Edge_container &edges)
void	cdt::ergodic_moves::detail::canonicalize (Vertex_container &vertices)
auto	cdt::ergodic_moves::detail::cell_precedes (Cell_handle const &left, Cell_handle const &right) -> bool
auto	cdt::ergodic_moves::detail::check_move (Manifold const &before, Manifold const &after, move_tracker::MoveType const &move) -> bool
	Check tracked move deltas and essential CDT manifold invariants.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::do_23_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Perform a (2,3) move.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::do_26_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Perform a (2,6) move.
template<std::uniform_random_bit_generator Generator, typename Post_mutation_validator>
auto	cdt::ergodic_moves::detail::do_26_move_impl (Manifold const &t_manifold, Generator &generator, bool const only_first_site, Post_mutation_validator post_mutation_validator) -> Expected
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::do_32_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Perform a (3,2) move.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::do_44_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Perform a (4,4) move.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::do_62_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Perform a (6,2) move.
auto	cdt::ergodic_moves::detail::edge_precedes (Edge_handle const &left, Edge_handle const &right) -> bool
auto	cdt::ergodic_moves::detail::execute (Delaunay &triangulation, ApplicableThreeTwoMove const &move) -> Execution
	Consume a prepared (3,2) value at the checked CGAL flip boundary.
template<typename Post_mutation_validator>
auto	cdt::ergodic_moves::detail::execute (Delaunay &triangulation, ApplicableTwoSixMove const &move, Post_mutation_validator post_mutation_validator) -> Execution
	Consume a prepared (2,6) value on an unobservable candidate.
auto	cdt::ergodic_moves::detail::execute (Delaunay &triangulation, ApplicableTwoThreeMove const &move) -> Execution
	Consume a prepared (2,3) value at the mutation boundary.
template<typename Post_mutation_validator>
auto	cdt::ergodic_moves::detail::execute (Delaunay const &source_triangulation, ApplicableFourFourMove const &move, Post_mutation_validator post_mutation_validator) -> std::expected< Delaunay, MoveError >
	Consume a prepared (4,4) value on a private triangulation copy.
template<std::uniform_random_bit_generator Generator, typename Post_mutation_validator>
auto	cdt::ergodic_moves::detail::execute (Delaunay const &source_triangulation, ApplicableSixTwoMove const &move, Generator &generator, Post_mutation_validator post_mutation_validator) -> std::expected< Delaunay, MoveError >
	Consume a prepared (6,2) value on a private triangulation copy.
auto	cdt::ergodic_moves::detail::find_adjacent_31_cell (Cell_handle const &cell) -> std::optional< int >
	Find a (2,6) move location.
auto	cdt::ergodic_moves::detail::find_bistellar_flip_location (Delaunay const &triangulation, Edge_handle const &candidate) -> std::optional< Cell_container >
	Find a bistellar flip location.
auto	cdt::ergodic_moves::detail::find_pivot_edge (Delaunay const &triangulation, Edge_container const &edges) -> std::optional< Edge_handle >
auto	cdt::ergodic_moves::detail::finite_incident_cells (Delaunay const &triangulation, Edge_handle const &edge) -> std::optional< Cell_container >
	Collect the finite cells incident to a checked edge.
auto	cdt::ergodic_moves::detail::get_vertices (Cell_container const &cells) -> Vertex_container
	Return a container of all vertices in a container of cells.
auto	cdt::ergodic_moves::detail::incident_cells_from_edge (Delaunay const &triangulation, Edge_handle const &edge) -> std::optional< Cell_container >
	Find all cells incident to the edge.
auto	cdt::ergodic_moves::detail::is_32_movable (Delaunay const &triangulation, Edge_handle const &candidate) -> bool
	Check for the causal cavity inverse to a (2,3) move.
auto	cdt::ergodic_moves::detail::is_62_movable (Delaunay const &triangulation, Vertex_handle const &candidate) -> bool
	Find a (6,2) move location.
auto	cdt::ergodic_moves::detail::is_well_formed_edge (Edge_handle const &edge) noexcept -> bool
	Check an edge handle without dereferencing its cell handle.
auto	cdt::ergodic_moves::detail::make_manifold (Delaunay triangulation, Manifold const &source) -> Manifold
	Rebuild all derived topology and geometry state around a value.
constexpr auto	cdt::ergodic_moves::detail::move_error (MoveFailure const reason, move_tracker::MoveType const move) noexcept -> std::unexpected< MoveError >
auto	cdt::ergodic_moves::null_move (Manifold const &t_manifold) -> Expected
	Perform a null move.
auto	cdt::ergodic_moves::detail::point_less (Point_t< 3 > const &left, Point_t< 3 > const &right) -> bool
auto	cdt::ergodic_moves::detail::prepare_bistellar_flip (Delaunay const &triangulation, Edge_handle const &candidate, Vertex_handle const &top, Vertex_handle const &bottom) -> std::expected< ApplicableFourFourMove, MoveError >
	Prepare the generic topological seam used by bistellar_flip().
auto	cdt::ergodic_moves::detail::prepare_four_four (Delaunay const &triangulation, Edge_handle const &candidate) -> std::expected< ApplicableFourFourMove, MoveError >
	Parse a raw spacelike edge into an applicable (4,4) move.
auto	cdt::ergodic_moves::detail::prepare_six_two (Delaunay const &triangulation, Vertex_handle const &candidate) -> std::expected< ApplicableSixTwoMove, MoveError >
	Parse a raw vertex into an applicable causal (6,2) move.
auto	cdt::ergodic_moves::detail::prepare_three_two (Delaunay const &triangulation, Edge_handle const &candidate) -> std::expected< ApplicableThreeTwoMove, MoveError >
	Parse a raw edge into an applicable causal (3,2) move.
auto	cdt::ergodic_moves::detail::prepare_two_six (Delaunay const &triangulation, Cell_handle const &candidate) -> std::expected< ApplicableTwoSixMove, MoveError >
	Parse a raw (1,3) cell into an applicable (2,6) move.
auto	cdt::ergodic_moves::detail::prepare_two_three (Delaunay const &triangulation, Cell_handle const &candidate) -> std::expected< ApplicableTwoThreeMove, MoveError >
	Parse a raw (2,2) cell into an applicable causal (2,3) move.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::propose_23_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Propose one (2,3) site for Metropolis-Hastings.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::propose_26_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Propose a uniformly selected (2,6) site.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::propose_32_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Propose one (3,2) site for Metropolis-Hastings.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::propose_44_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Propose one spacelike edge as a (4,4) site.
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::propose_62_move (Manifold const &t_manifold, Generator &generator) -> Expected
	Propose one vertex as a (6,2) site for Metropolis-Hastings.
template<typename Container, std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::detail::random_element (Container const &candidates, Generator &generator) -> std::optional< typename Container::value_type >
	Select exactly one raw proposal site uniformly in container order.
auto	cdt::ergodic_moves::detail::resolve_cell (Delaunay const &triangulation, Cell_points const &points) -> std::optional< Cell_handle >
auto	cdt::ergodic_moves::detail::resolve_edge (Delaunay const &triangulation, Edge_points const &points) -> std::optional< Edge_handle >
auto	cdt::ergodic_moves::detail::resolve_vertex (Delaunay const &triangulation, Point_t< 3 > const &point) -> std::optional< Vertex_handle >
auto	cdt::ergodic_moves::detail::same_configuration_value (double const first, double const second) noexcept -> bool
	Compare preserved floating-point configuration state exactly.
auto	cdt::ergodic_moves::detail::try_23_move (Delaunay &triangulation, Cell_handle const &to_be_moved) -> bool
	Compatibility seam that prepares and immediately executes (2,3).
auto	cdt::ergodic_moves::detail::try_32_move (Delaunay &triangulation, Edge_handle const &to_be_moved) -> bool
	Compatibility seam that prepares and immediately executes (3,2).
template<std::uniform_random_bit_generator Generator>
auto	cdt::ergodic_moves::detail::try_62_move (Delaunay const &source_triangulation, Vertex_handle const source_candidate, Generator &generator) -> std::optional< Delaunay >
	Apply the combinatorial (6,2) retriangulation on a private copy.
template<std::uniform_random_bit_generator Generator, typename Post_mutation_validator>
auto	cdt::ergodic_moves::detail::try_62_move_impl (Delaunay const &source_triangulation, Vertex_handle const source_candidate, Generator &generator, Post_mutation_validator post_mutation_validator) -> std::optional< Delaunay >
auto	cdt::ergodic_moves::detail::vertex_precedes (Vertex_handle const &left, Vertex_handle const &right) -> bool

Detailed Description

Pachner moves on 2+1 dimensional foliated Delaunay triangulations.

Author: Adam Getchell

Pachner moves operate on the level of the Manifold_3. The helper functions for the moves operate on the level of the Delaunay_Triangulation_3. C++23 support is required for std::expected.

See also: Pachner moves; Three-dimensional CDT move set; 2+1D CDT ergodic move audit

Definition in file Ergodic_moves_3.hpp.

Typedef Documentation

◆ Cell_container

using cdt::ergodic_moves::Cell_container = std::vector<Cell_handle>

Collection of three-dimensional cell handles.

Definition at line 50 of file Ergodic_moves_3.hpp.

◆ Cell_handle

using cdt::ergodic_moves::Cell_handle = Cell_handle_t<3>

Three-dimensional CGAL cell handle.

Definition at line 48 of file Ergodic_moves_3.hpp.

◆ Cell_points

using cdt::ergodic_moves::detail::Cell_points = std::array<Point_t<3>, 4>

Definition at line 64 of file Ergodic_moves_3.hpp.

◆ Delaunay

using cdt::ergodic_moves::Delaunay = Delaunay_t<3>

Three-dimensional Delaunay triangulation used by move implementations.

Definition at line 60 of file Ergodic_moves_3.hpp.

◆ Edge_container

using cdt::ergodic_moves::Edge_container = std::vector<Edge_handle>

Collection of three-dimensional edge descriptors.

Definition at line 54 of file Ergodic_moves_3.hpp.

◆ Edge_handle

using cdt::ergodic_moves::Edge_handle = Edge_handle_t<3>

Three-dimensional CGAL edge descriptor.

Definition at line 52 of file Ergodic_moves_3.hpp.

◆ Edge_points

using cdt::ergodic_moves::detail::Edge_points = std::array<Point_t<3>, 2>

Definition at line 65 of file Ergodic_moves_3.hpp.

◆ Execution

using cdt::ergodic_moves::detail::Execution = std::expected<void, MoveError>

Definition at line 66 of file Ergodic_moves_3.hpp.

◆ Expected

using cdt::ergodic_moves::Expected = MoveResult<Manifold>

Fallible manifold transformation returned by public move functions.

Definition at line 46 of file Ergodic_moves_3.hpp.

◆ Manifold

using cdt::ergodic_moves::Manifold = manifolds::Manifold_3

Three-dimensional spherical CDT manifold operated on by this move set.

Definition at line 44 of file Ergodic_moves_3.hpp.

◆ Vertex_container

using cdt::ergodic_moves::Vertex_container = std::vector<Vertex_handle>

Collection of three-dimensional vertex handles.

Definition at line 58 of file Ergodic_moves_3.hpp.

◆ Vertex_handle

using cdt::ergodic_moves::Vertex_handle = Vertex_handle_t<3>

Three-dimensional CGAL vertex handle.

Definition at line 56 of file Ergodic_moves_3.hpp.

Function Documentation

◆ accept_post_mutation()

auto cdt::ergodic_moves::detail::accept_post_mutation ( Delaunay const & triangulation ) -> bool

inlinenodiscardnoexcept

Default validator for internal post-mutation test seams.

Definition at line 195 of file Ergodic_moves_3.hpp.

◆ bistellar_flip()

auto cdt::ergodic_moves::detail::bistellar_flip	(	Delaunay const &	source_triangulation,
		Edge_handle	source_edge,
		Vertex_handle	source_top,
		Vertex_handle	source_bottom ) -> std::optional< Delaunay >

inlinenodiscard

Perform a bistellar flip on triangulation via the given edge.

Pass by value to avoid modifying the original triangulation in the event that the flip is unsuccessful.

Parameters

source_triangulation	The triangulation to flip
source_edge	The edge to pivot on
source_top	Top vertex of the cells being flipped
source_bottom	Bottom vertex of the cells being flipped

Returns: A flipped triangulation or nullopt

See also: Pachner moves

Definition at line 1756 of file Ergodic_moves_3.hpp.

◆ bistellar_flip_impl()

template<typename Post_mutation_validator>

auto cdt::ergodic_moves::detail::bistellar_flip_impl	(	Delaunay const &	source_triangulation,
		Edge_handle const	source_edge,
		Vertex_handle const	source_top,
		Vertex_handle const	source_bottom,
		Post_mutation_validator	post_mutation_validator ) -> std::optional< Delaunay >

inlinenodiscard

Definition at line 1732 of file Ergodic_moves_3.hpp.

◆ canonical_cell_points()

auto cdt::ergodic_moves::detail::canonical_cell_points ( Cell_handle const & cell ) -> std::array< Point_t< 3 >, 4 >

inlinenodiscard

Definition at line 252 of file Ergodic_moves_3.hpp.

◆ canonical_edge_descriptor()

auto cdt::ergodic_moves::detail::canonical_edge_descriptor	(	Delaunay const &	triangulation,
		Edge_handle const &	edge ) -> std::optional< Edge_handle >

inlinenodiscard

Rebind an edge to its canonical finite incident cell.

CGAL permits any incident cell to own an edge descriptor, but checked flips can observe that representative. Choosing by canonical cell points makes equivalent in-memory and reloaded triangulations use the same mutation boundary.

Definition at line 355 of file Ergodic_moves_3.hpp.

◆ canonical_edge_points()

auto cdt::ergodic_moves::detail::canonical_edge_points ( Edge_handle const & edge ) -> std::array< Point_t< 3 >, 2 >

inlinenodiscard

Definition at line 261 of file Ergodic_moves_3.hpp.

◆ canonical_random_element() [1/4]

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::detail::canonical_random_element	(	Cell_container &	cells,
		Generator &	generator ) -> std::optional< Cell_handle >

inlinenodiscard

Definition at line 417 of file Ergodic_moves_3.hpp.

◆ canonical_random_element() [2/4]

template<typename Container, std::uniform_random_bit_generator Generator, typename Comparator>

auto cdt::ergodic_moves::detail::canonical_random_element	(	Container &	candidates,
		Generator &	generator,
		Comparator	comparator ) -> std::optional< typename Container::value_type >

inlinenodiscard

Select the same canonical rank as sorting followed by indexed selection, without sorting the complete proposal domain.

Definition at line 401 of file Ergodic_moves_3.hpp.

◆ canonical_random_element() [3/4]

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::detail::canonical_random_element	(	Edge_container &	edges,
		Generator &	generator ) -> std::optional< Edge_handle >

inlinenodiscard

Definition at line 423 of file Ergodic_moves_3.hpp.

◆ canonical_random_element() [4/4]

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::detail::canonical_random_element	(	Vertex_container &	vertices,
		Generator &	generator ) -> std::optional< Vertex_handle >

inlinenodiscard

Definition at line 429 of file Ergodic_moves_3.hpp.

◆ canonicalize() [1/3]

void cdt::ergodic_moves::detail::canonicalize ( Cell_container & cells )

inline

Definition at line 337 of file Ergodic_moves_3.hpp.

◆ canonicalize() [2/3]

void cdt::ergodic_moves::detail::canonicalize ( Edge_container & edges )

inline

Definition at line 340 of file Ergodic_moves_3.hpp.

◆ canonicalize() [3/3]

void cdt::ergodic_moves::detail::canonicalize ( Vertex_container & vertices )

inline

Definition at line 343 of file Ergodic_moves_3.hpp.

◆ cell_precedes()

auto cdt::ergodic_moves::detail::cell_precedes	(	Cell_handle const &	left,
		Cell_handle const &	right ) -> bool

inlinenodiscard

Definition at line 319 of file Ergodic_moves_3.hpp.

◆ check_move()

auto cdt::ergodic_moves::detail::check_move	(	Manifold const &	t_before,
		Manifold const &	t_after,
		move_tracker::MoveType const &	t_move ) -> bool

inlinenodiscard

Check tracked move deltas and essential CDT manifold invariants.

This verifies structural cache counts, causal foliation, cell metadata, TDS validity, geometry deltas, time bounds, and preserved foliation parameters without rebuilding derived caches. It does not require Euclidean Delaunayhood.

Parameters

t_before	The manifold before the move
t_after	The manifold after the move
t_move	The type of move

Returns: True if the move correctly changed the triangulation

Definition at line 1903 of file Ergodic_moves_3.hpp.

◆ do_23_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::do_23_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Perform a (2,3) move.

A (2,3) move "flips" a timelike face into a timelike edge. This adds a (2,2) simplex and a timelike edge.

This function calls try_23_move on (2,2) simplices drawn from a randomly shuffled container until it succeeds or runs out of simplices.

The move guarantees a valid causal combinatorial triangulation. It does not preserve or require the empty-sphere property of the coordinates.

Template Parameters

Generator A uniform random bit generator type

Parameters

t_manifold	The simplicial manifold
generator	Caller-owned generator whose state advances during the move

Returns: The Expected (2,3) moved manifold or an Unexpected

Note: The source manifold is unchanged on success and failure.

Definition at line 674 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_cells(), cdt::foliated_triangulations::filter_cells(), and cdt::TWO_TWO.

◆ do_26_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::do_26_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Perform a (2,6) move.

A (2,6) move inserts a vertex into the spacelike face between a (1,3) simplex on the bottom connected to a (3,1) simplex on top. This adds 2 (1,3) simplices and 2 (3,1) simplices. It adds 2 spacelike faces and 6 timelike faces. It also adds 2 timelike edges and 3 spacelike edges, as well as the vertex. This function calls find_adjacent_31_cell on (1,3) simplices drawn from a randomly shuffled container until it succeeds or runs out of simplices. The move guarantees a valid causal combinatorial triangulation. It does not preserve or require the empty-sphere property of the coordinates.

Template Parameters

Generator A uniform random bit generator type

Parameters

t_manifold	The simplicial manifold
generator	Caller-owned generator whose state advances during the move

Returns: The Expected (2,6) moved manifold or an Unexpected

Note: The source manifold is unchanged on success and failure.

Definition at line 1152 of file Ergodic_moves_3.hpp.

◆ do_26_move_impl()

template<std::uniform_random_bit_generator Generator, typename Post_mutation_validator>

auto cdt::ergodic_moves::detail::do_26_move_impl	(	Manifold const &	t_manifold,
		Generator &	generator,
		bool const	only_first_site,
		Post_mutation_validator	post_mutation_validator ) -> Expected

inlinenodiscard

Definition at line 1079 of file Ergodic_moves_3.hpp.

◆ do_32_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::do_32_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Perform a (3,2) move.

A (3,2) move "flips" a timelike edge into a timelike face. This removes a (2,2) simplex and the timelike edge. This function calls try_32_move on timelike edges drawn from a randomly shuffled container until it succeeds or runs out of edges. The move guarantees a valid causal combinatorial triangulation. It does not preserve or require the empty-sphere property of the coordinates.

Template Parameters

Generator A uniform random bit generator type

Parameters

t_manifold	The simplicial manifold
generator	Caller-owned generator whose state advances during the move

Returns: The Expected (3,2) moved manifold or an Unexpected

Note: The source manifold is unchanged on success and failure.

Definition at line 843 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_edges(), cdt::foliated_triangulations::filter_edges(), and cdt::TIMELIKE.

◆ do_44_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::do_44_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Perform a (4,4) move.

This is a bistellar flip pivoting the internal spacelike edge between the two spacelike faces. A (4,4) move flips an edge which has exactly 4 incident cells. In CDT specifically, the edge is spacelike and the 4 incident cells are a pair of (1,3) simplices and a pair of (3,1) simplices. It thus re-labels each of the 4 cells in the complex, but doesn't actually change the number of cells, vertices, or edges. This move has the effect of mixing up the simplices, thus possibly creating different potential moves in different locations.

This function calls is_44_movable() on a randomly shuffled container of edges until it succeeds or runs out of edges.

If successful, the triangulation remains combinatorially valid. A CDT move is not required to preserve the Euclidean Delaunay property of the coordinates used to represent the abstract triangulation.

Template Parameters

Generator A uniform random bit generator type

Parameters

t_manifold	The simplicial manifold
generator	Caller-owned generator whose state advances during the move

Returns: The Expected (4,4) moved manifold or Unexpected

Note: The source manifold is unchanged on success and failure.

Definition at line 1822 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_edges(), cdt::foliated_triangulations::filter_edges(), and cdt::SPACELIKE.

◆ do_62_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::do_62_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Perform a (6,2) move.

This function performs a (6,2) move on the given manifold. A (6,2) move removes a vertex which has 3 incident (3,1) simplices and 3 (1,3) simplices for a total of 6 incident simplices exactly. This converts the 3 (1,3) simplices into a single (1,3) simplex on the bottom and the 3 (3,1) simplices into a single (3,1) simplex on top. It thus removes 2 (1,3) simplices, 2 (3,1) simplices, 2 spacelike faces, 6 timelike faces, 3 spacelike edges, 2 timelike edges, and a single vertex.

This function calls is_62_movable() on a randomly shuffled container of vertices until it succeeds or runs out of vertices.

The move guarantees a valid causal combinatorial triangulation. It does not preserve or require the empty-sphere property of the coordinates.

Template Parameters

Generator A uniform random bit generator type

Parameters

t_manifold	The simplicial manifold
generator	Caller-owned generator whose state advances during the move

Returns: The Expected (6,2) moved manifold or Unexpected

Note: The source manifold is unchanged on success and failure.

Definition at line 1404 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_vertices().

◆ edge_precedes()

auto cdt::ergodic_moves::detail::edge_precedes	(	Edge_handle const &	left,
		Edge_handle const &	right ) -> bool

inlinenodiscard

Definition at line 328 of file Ergodic_moves_3.hpp.

◆ execute() [1/5]

auto cdt::ergodic_moves::detail::execute	(	Delaunay &	triangulation,
		ApplicableThreeTwoMove const &	move ) -> Execution

inlinenodiscard

Consume a prepared (3,2) value at the checked CGAL flip boundary.

Definition at line 803 of file Ergodic_moves_3.hpp.

◆ execute() [2/5]

template<typename Post_mutation_validator>

auto cdt::ergodic_moves::detail::execute	(	Delaunay &	triangulation,
		ApplicableTwoSixMove const &	move,
		Post_mutation_validator	post_mutation_validator ) -> Execution

inlinenodiscard

Consume a prepared (2,6) value on an unobservable candidate.

Local mutation is deliberate. Any postcondition failure discards the private triangulation at the high-level value boundary.

Definition at line 993 of file Ergodic_moves_3.hpp.

◆ execute() [3/5]

auto cdt::ergodic_moves::detail::execute	(	Delaunay &	triangulation,
		ApplicableTwoThreeMove const &	move ) -> Execution

inlinenodiscard

Consume a prepared (2,3) value at the mutation boundary.

Only point-to-handle resolution is repeated. CDT applicability is carried by the input type; CGAL remains responsible for its checked geometric flip. A successful flip invalidates affected cell handles, none of which are stored in the applicable value.

Definition at line 615 of file Ergodic_moves_3.hpp.

◆ execute() [4/5]

template<typename Post_mutation_validator>

auto cdt::ergodic_moves::detail::execute	(	Delaunay const &	source_triangulation,
		ApplicableFourFourMove const &	move,
		Post_mutation_validator	post_mutation_validator ) -> std::expected< Delaunay, MoveError >

inlinenodiscard

Consume a prepared (4,4) value on a private triangulation copy.

Definition at line 1640 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::expected_cell_type().

◆ execute() [5/5]

template<std::uniform_random_bit_generator Generator, typename Post_mutation_validator>

auto cdt::ergodic_moves::detail::execute	(	Delaunay const &	source_triangulation,
		ApplicableSixTwoMove const &	move,
		Generator &	generator,
		Post_mutation_validator	post_mutation_validator ) -> std::expected< Delaunay, MoveError >

inlinenodiscard

Consume a prepared (6,2) value on a private triangulation copy.

Definition at line 1274 of file Ergodic_moves_3.hpp.

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

◆ find_adjacent_31_cell()

auto cdt::ergodic_moves::detail::find_adjacent_31_cell ( Cell_handle const & t_cell ) -> std::optional< int >

inlinenodiscard

Find a (2,6) move location.

This function checks to see if a (2,6) move is possible. Starting with a (1,3) simplex, it checks neighbors for a (3,1) simplex.

Parameters

t_cell The (1,3) simplex that is checked

Returns: The integer of the neighboring (3,1) simplex or nullopt

Definition at line 914 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::expected_cell_type(), cdt::foliated_triangulations::is_cell_type_correct(), cdt::ONE_THREE, and cdt::THREE_ONE.

◆ find_bistellar_flip_location()

auto cdt::ergodic_moves::detail::find_bistellar_flip_location	(	Delaunay const &	triangulation,
		Edge_handle const &	t_edge_candidate ) -> std::optional< Cell_container >

inlinenodiscard

Find a bistellar flip location.

This function checks to see if a bistellar flip is possible. Starting with an edge, it checks all incident cells. There must be 4 incident cells; 2 should be (3,1) simplices, 2 should be (1,3) simplices, and there should be no (2,2) simplices.

Parameters

triangulation	The simplicial manifold
t_edge_candidate	The edge to check

Returns: A container of incident cells if there are exactly 4 or nullopt

Definition at line 1488 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::expected_cell_type(), cdt::foliated_triangulations::is_cell_type_correct(), cdt::ONE_THREE, and cdt::THREE_ONE.

◆ find_pivot_edge()

auto cdt::ergodic_moves::detail::find_pivot_edge	(	Delaunay const &	triangulation,
		Edge_container const &	edges ) -> std::optional< Edge_handle >

inlinenodiscard

Returns: The center edge of a 4-cell complex

Definition at line 1767 of file Ergodic_moves_3.hpp.

◆ finite_incident_cells()

auto cdt::ergodic_moves::detail::finite_incident_cells	(	Delaunay const &	triangulation,
		Edge_handle const &	edge ) -> std::optional< Cell_container >

inlinenodiscard

Collect the finite cells incident to a checked edge.

The returned handles borrow from triangulation and remain valid only until an affected-cell mutation is performed.

Definition at line 227 of file Ergodic_moves_3.hpp.

◆ get_vertices()

auto cdt::ergodic_moves::detail::get_vertices ( Cell_container const & cells ) -> Vertex_container

inlinenodiscard

Return a container of all vertices in a container of cells.

Parameters

cells The cells to find the vertices of.

Returns: A container of vertices in the cells

Definition at line 1785 of file Ergodic_moves_3.hpp.

◆ incident_cells_from_edge()

auto cdt::ergodic_moves::detail::incident_cells_from_edge	(	Delaunay const &	triangulation,
		Edge_handle const &	edge ) -> std::optional< Cell_container >

inlinenodiscard

Find all cells incident to the edge.

Parameters

triangulation	The Delaunay triangulation
edge	The edge

Returns: A container of cells incident to the edge or nullopt

See also: https://github.com/CGAL/cgal/blob/8430d04539179f25fb8e716f99e19d28589beeda/TDS_3/include/CGAL/Triangulation_data_structure_3.h#L2094

Definition at line 1473 of file Ergodic_moves_3.hpp.

◆ is_32_movable()

auto cdt::ergodic_moves::detail::is_32_movable	(	Delaunay const &	triangulation,
		Edge_handle const &	candidate ) -> bool

inlinenodiscard

Check for the causal cavity inverse to a (2,3) move.

Definition at line 743 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::expected_cell_type(), cdt::foliated_triangulations::is_cell_type_correct(), cdt::ONE_THREE, cdt::THREE_ONE, and cdt::TWO_TWO.

◆ is_62_movable()

auto cdt::ergodic_moves::detail::is_62_movable	(	Delaunay const &	triangulation,
		Vertex_handle const &	candidate ) -> bool

inlinenodiscard

Find a (6,2) move location.

This function checks to see if a (6,2) move is possible. Starting with a vertex, it checks all incident cells. There must be 6 incident cells; 3 should be (3,1) simplices, 3 should be (1,3) simplices, and there should be no (2,2) simplices.

Parameters

triangulation	The triangulation containing the candidate
candidate	The vertex to check

Returns: True if (6,2) move is possible

Definition at line 1183 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::expected_cell_type(), cdt::foliated_triangulations::is_cell_type_correct(), cdt::ONE_THREE, cdt::THREE_ONE, and cdt::TWO_TWO.

◆ is_well_formed_edge()

auto cdt::ergodic_moves::detail::is_well_formed_edge ( Edge_handle const & edge ) -> bool

inlinenodiscardnoexcept

Check an edge handle without dereferencing its cell handle.

A tetrahedral cell has four local vertex indices in [0, 4).

Definition at line 212 of file Ergodic_moves_3.hpp.

◆ make_manifold()

auto cdt::ergodic_moves::detail::make_manifold	(	Delaunay	triangulation,
		Manifold const &	source ) -> Manifold

inlinenodiscard

Rebuild all derived topology and geometry state around a value.

Definition at line 200 of file Ergodic_moves_3.hpp.

◆ move_error()

auto cdt::ergodic_moves::detail::move_error	(	MoveFailure const	reason,
		move_tracker::MoveType const	move ) -> std::unexpected< MoveError >

nodiscardconstexprnoexcept

Definition at line 174 of file Ergodic_moves_3.hpp.

◆ null_move()

auto cdt::ergodic_moves::null_move ( Manifold const & t_manifold ) -> Expected

inlinenodiscard

Perform a null move.

Parameters

t_manifold The simplicial manifold

Returns: The null-moved manifold

Definition at line 545 of file Ergodic_moves_3.hpp.

◆ point_less()

auto cdt::ergodic_moves::detail::point_less	(	Point_t< 3 > const &	left,
		Point_t< 3 > const &	right ) -> bool

inlinenodiscard

Definition at line 248 of file Ergodic_moves_3.hpp.

◆ prepare_bistellar_flip()

auto cdt::ergodic_moves::detail::prepare_bistellar_flip	(	Delaunay const &	triangulation,
		Edge_handle const &	candidate,
		Vertex_handle const &	top,
		Vertex_handle const &	bottom ) -> std::expected< ApplicableFourFourMove, MoveError >

inlinenodiscard

Prepare the generic topological seam used by bistellar_flip().

Unlike prepare_four_four(), this internal compatibility boundary proves only the CGAL four-cell diamond and caller-supplied boundary vertices. High-level CDT moves must use the stronger causal preparation.

Definition at line 1581 of file Ergodic_moves_3.hpp.

◆ prepare_four_four()

auto cdt::ergodic_moves::detail::prepare_four_four	(	Delaunay const &	triangulation,
		Edge_handle const &	candidate ) -> std::expected< ApplicableFourFourMove, MoveError >

inlinenodiscard

Parse a raw spacelike edge into an applicable (4,4) move.

Success proves the finite four-cell causal diamond and identifies its distinct top and bottom vertices without retaining CGAL handles.

Definition at line 1520 of file Ergodic_moves_3.hpp.

◆ prepare_six_two()

auto cdt::ergodic_moves::detail::prepare_six_two	(	Delaunay const &	triangulation,
		Vertex_handle const &	candidate ) -> std::expected< ApplicableSixTwoMove, MoveError >

inlinenodiscard

Parse a raw vertex into an applicable causal (6,2) move.

Success proves degree five, six finite incident cells, and the exact three-(3,1)/three-(1,3) causal composition with correct metadata.

Definition at line 1239 of file Ergodic_moves_3.hpp.

◆ prepare_three_two()

auto cdt::ergodic_moves::detail::prepare_three_two	(	Delaunay const &	triangulation,
		Edge_handle const &	candidate ) -> std::expected< ApplicableThreeTwoMove, MoveError >

inlinenodiscard

Parse a raw edge into an applicable causal (3,2) move.

Success proves a finite timelike degree-three cavity containing exactly two (2,2) cells and one consistently oriented (3,1) or (1,3) cell.

Definition at line 784 of file Ergodic_moves_3.hpp.

◆ prepare_two_six()

auto cdt::ergodic_moves::detail::prepare_two_six	(	Delaunay const &	triangulation,
		Cell_handle const &	candidate ) -> std::expected< ApplicableTwoSixMove, MoveError >

inlinenodiscard

Parse a raw (1,3) cell into an applicable (2,6) move.

Success proves a correctly labelled adjacent (3,1) cell and a common spacelike facet whose three vertices share one time value.

Definition at line 951 of file Ergodic_moves_3.hpp.

◆ prepare_two_three()

auto cdt::ergodic_moves::detail::prepare_two_three	(	Delaunay const &	triangulation,
		Cell_handle const &	candidate ) -> std::expected< ApplicableTwoThreeMove, MoveError >

inlinenodiscard

Parse a raw (2,2) cell into an applicable causal (2,3) move.

Success proves that the selected finite cell has correct metadata, has a correctly classified (3,1) or (1,3) neighbor, and that the two vertices opposite their shared facet span adjacent slices. The returned value owns only stable point locators and must be executed against the same unmodified triangulation.

Definition at line 554 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::expected_cell_type(), cdt::foliated_triangulations::is_cell_type_correct(), cdt::ONE_THREE, cdt::THREE_ONE, and cdt::TWO_TWO.

◆ propose_23_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::propose_23_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Propose one (2,3) site for Metropolis-Hastings.

Unlike do_23_move(), this samples exactly one of the N3(2,2) cells. An inapplicable selected cell is a rejected proposal rather than a reason to condition the proposal distribution on the movable subset.

Template Parameters

Generator Uniform random bit generator type.

Parameters

t_manifold	Source manifold, which remains unchanged.
generator	Caller-owned generator advanced by site sampling.

Returns: Proposed manifold, or a structured reason the site was rejected.

Definition at line 720 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_cells(), cdt::foliated_triangulations::filter_cells(), and cdt::TWO_TWO.

◆ propose_26_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::propose_26_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Propose a uniformly selected (2,6) site.

Exactly one uniformly selected (1,3) cell is examined. An inapplicable raw site is returned as a failed proposal so Metropolis- Hastings can account for it as a self-transition.

Template Parameters

Generator Uniform random bit generator type.

Parameters

t_manifold	Source manifold, which remains unchanged.
generator	Caller-owned generator advanced by site sampling.

Returns: Proposed manifold, or a structured reason the site was rejected.

Definition at line 1168 of file Ergodic_moves_3.hpp.

◆ propose_32_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::propose_32_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Propose one (3,2) site for Metropolis-Hastings.

The raw proposal domain is the set of timelike edges. Selecting a nonflippable edge produces a self-transition.

Template Parameters

Generator Uniform random bit generator type.

Parameters

t_manifold	Source manifold, which remains unchanged.
generator	Caller-owned generator advanced by site sampling.

Returns: Proposed manifold, or a structured reason the site was rejected.

Definition at line 888 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_edges(), cdt::foliated_triangulations::filter_edges(), and cdt::TIMELIKE.

◆ propose_44_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::propose_44_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Propose one spacelike edge as a (4,4) site.

Selecting an edge that is not the pivot of a causal four-cell complex is an explicit self-transition.

Template Parameters

Generator Uniform random bit generator type.

Parameters

t_manifold	Source manifold, which remains unchanged.
generator	Caller-owned generator advanced by site sampling.

Returns: Proposed manifold, or a structured reason the site was rejected.

Definition at line 1868 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_edges(), cdt::foliated_triangulations::filter_edges(), and cdt::SPACELIKE.

◆ propose_62_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::propose_62_move	(	Manifold const &	t_manifold,
		Generator &	generator ) -> Expected

inlinenodiscard

Propose one vertex as a (6,2) site for Metropolis-Hastings.

Template Parameters

Generator Uniform random bit generator type.

Parameters

t_manifold	Source manifold, which remains unchanged.
generator	Caller-owned generator advanced by site sampling and ordering incident-edge flip paths.

Returns: Proposed manifold, or a structured reason the site was rejected.

Definition at line 1447 of file Ergodic_moves_3.hpp.

References cdt::foliated_triangulations::collect_vertices().

◆ random_element()

template<typename Container, std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::detail::random_element	(	Container const &	candidates,
		Generator &	generator ) -> std::optional< typename Container::value_type >

inlinenodiscard

Select exactly one raw proposal site uniformly in container order.

Definition at line 387 of file Ergodic_moves_3.hpp.

◆ resolve_cell()

auto cdt::ergodic_moves::detail::resolve_cell	(	Delaunay const &	triangulation,
		Cell_points const &	points ) -> std::optional< Cell_handle >

inlinenodiscard

Definition at line 279 of file Ergodic_moves_3.hpp.

◆ resolve_edge()

auto cdt::ergodic_moves::detail::resolve_edge	(	Delaunay const &	triangulation,
		Edge_points const &	points ) -> std::optional< Edge_handle >

inlinenodiscard

Definition at line 300 of file Ergodic_moves_3.hpp.

◆ resolve_vertex()

auto cdt::ergodic_moves::detail::resolve_vertex	(	Delaunay const &	triangulation,
		Point_t< 3 > const &	point ) -> std::optional< Vertex_handle >

inlinenodiscard

Definition at line 270 of file Ergodic_moves_3.hpp.

◆ same_configuration_value()

auto cdt::ergodic_moves::detail::same_configuration_value	(	double const	first,
		double const	second ) -> bool

inlinenodiscardnoexcept

Compare preserved floating-point configuration state exactly.

Move construction copies these values; arithmetic tolerance is inappropriate because any representation change indicates state drift.

Definition at line 186 of file Ergodic_moves_3.hpp.

◆ try_23_move()

auto cdt::ergodic_moves::detail::try_23_move	(	Delaunay &	triangulation,
		Cell_handle const &	to_be_moved ) -> bool

inlinenodiscard

Compatibility seam that prepares and immediately executes (2,3).

Definition at line 648 of file Ergodic_moves_3.hpp.

◆ try_32_move()

auto cdt::ergodic_moves::detail::try_32_move	(	Delaunay &	triangulation,
		Edge_handle const &	to_be_moved ) -> bool

inlinenodiscard

Compatibility seam that prepares and immediately executes (3,2).

Definition at line 821 of file Ergodic_moves_3.hpp.

◆ try_62_move()

template<std::uniform_random_bit_generator Generator>

auto cdt::ergodic_moves::detail::try_62_move	(	Delaunay const &	source_triangulation,
		Vertex_handle const	source_candidate,
		Generator &	generator ) -> std::optional< Delaunay >

inlinenodiscard

Apply the combinatorial (6,2) retriangulation on a private copy.

A (3,2) flip of either timelike edge incident to the removable vertex leaves that vertex with degree four. Removing it from its maximal simplex then replaces the original six cells with the required two cells. Keeping both operations in a private copy makes rejection failure-atomic.

Parameters

source_triangulation	The triangulation containing the candidate
source_candidate	The degree-five vertex to remove
generator	The caller-owned random engine used to order flip paths

Returns: The moved triangulation, or nullopt when the topology is not flippable or the result violates a triangulation or causal-cell invariant

Definition at line 1372 of file Ergodic_moves_3.hpp.

◆ try_62_move_impl()

template<std::uniform_random_bit_generator Generator, typename Post_mutation_validator>

auto cdt::ergodic_moves::detail::try_62_move_impl	(	Delaunay const &	source_triangulation,
		Vertex_handle const	source_candidate,
		Generator &	generator,
		Post_mutation_validator	post_mutation_validator ) -> std::optional< Delaunay >

inlinenodiscard

Definition at line 1346 of file Ergodic_moves_3.hpp.

◆ vertex_precedes()

auto cdt::ergodic_moves::detail::vertex_precedes	(	Vertex_handle const &	left,
		Vertex_handle const &	right ) -> bool

inlinenodiscard

Definition at line 374 of file Ergodic_moves_3.hpp.

Namespaces

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ Cell_container

◆ Cell_handle

◆ Cell_points

◆ Delaunay

◆ Edge_container

◆ Edge_handle

◆ Edge_points

◆ Execution

◆ Expected

◆ Manifold

◆ Vertex_container

◆ Vertex_handle

Function Documentation

◆ accept_post_mutation()

◆ bistellar_flip()

◆ bistellar_flip_impl()

◆ canonical_cell_points()

◆ canonical_edge_descriptor()

◆ canonical_edge_points()

◆ canonical_random_element() [1/4]

◆ canonical_random_element() [2/4]

◆ canonical_random_element() [3/4]

◆ canonical_random_element() [4/4]

◆ canonicalize() [1/3]

◆ canonicalize() [2/3]

◆ canonicalize() [3/3]

◆ cell_precedes()

◆ check_move()

◆ do_23_move()

◆ do_26_move()

◆ do_26_move_impl()

◆ do_32_move()

◆ do_44_move()

◆ do_62_move()

◆ edge_precedes()

◆ execute() [1/5]

◆ execute() [2/5]

◆ execute() [3/5]

◆ execute() [4/5]

◆ execute() [5/5]

◆ find_adjacent_31_cell()

◆ find_bistellar_flip_location()

◆ find_pivot_edge()

◆ finite_incident_cells()

◆ get_vertices()

◆ incident_cells_from_edge()

◆ is_32_movable()

◆ is_62_movable()

◆ is_well_formed_edge()

◆ make_manifold()

◆ move_error()

◆ null_move()

◆ point_less()

◆ prepare_bistellar_flip()

◆ prepare_four_four()

◆ prepare_six_two()

◆ prepare_three_two()

◆ prepare_two_six()

◆ prepare_two_three()

◆ propose_23_move()

◆ propose_26_move()

◆ propose_32_move()

◆ propose_44_move()

◆ propose_62_move()

◆ random_element()

◆ resolve_cell()

◆ resolve_edge()

◆ resolve_vertex()

◆ same_configuration_value()

◆ try_23_move()

◆ try_32_move()

◆ try_62_move()

◆ try_62_move_impl()

◆ vertex_precedes()