clang-15 does not support std::format More...

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

Classes
struct	Geometry
struct	Geometry< 3 >
	3D Geometry More...
class	MoveCommand
	Queue and execute requested moves against a three-dimensional manifold while tracking attempted and successful transitions. More...
class	MoveRunCadence
	Positive pass count and checkpoint interval for a move run. More...
class	MoveStrategy
	Select a move algorithm. More...
class	MoveStrategy< MoveStrategyKind::METROPOLIS, ManifoldType >
	Metropolis-Hastings algorithm strategy. More...
class	MoveStrategy< MoveStrategyKind::MOVE_ALWAYS, ManifoldType >
	The Move Always algorithm. More...
class	Random
	A run-owned PCG engine with a recorded seed and stream identifier. More...
class	RandomSeed
	Root entropy value used to reproduce a random run. More...
class	RandomStream
	PCG sequence selector derived from a root random seed. More...

Concepts
concept	ConstForwardRange
	A multi-pass range whose const-qualified value can be traversed by classification and materialization helpers.

Typedefs
template<int dimension>
using	Causal_vertices_t
	Point/time-label pairs used to build a causal triangulation.
template<int dimension>
using	Cell_handle_t
	Mutable CGAL cell handle for a triangulation dimension.
template<int dimension>
using	Delaunay_t = typename detail::TriangulationTraits<dimension>::Delaunay
	Delaunay triangulation type for dimension spatial dimensions.
template<int dimension>
using	Edge_handle_t
	CGAL edge descriptor for a triangulation dimension.
template<int dimension>
using	Facet_t = typename detail::TriangulationTraits<dimension>::Facet
	CGAL facet descriptor for a triangulation dimension.
using	Geometry_3 = Geometry<3>
	Three-dimensional simplex-count geometry.
using	Gmpzf = CGAL::Gmpzf
using	Int_precision = std::int32_t
using	Metropolis_3
	Metropolis-Hastings move strategy for the supported 3D manifold.
using	MoveAlways_3
	Always-accept-applicable move strategy for the supported 3D manifold.
template<int dimension>
using	Point_t = typename detail::TriangulationTraits<dimension>::Point
	Cartesian point type used by a triangulation dimension.
template<int dimension>
using	Spherical_points_generator_t
	CGAL random point generator on a sphere of matching dimension.
template<int dimension>
using	Vertex_handle_t
	Mutable CGAL vertex handle for a triangulation dimension.

Enumerations
enum class	CellType { THREE_ONE = 31 , TWO_TWO = 22 , ONE_THREE = 13 , ACAUSAL = 99 , UNCLASSIFIED = 0 }
	(n,m) is number of vertices on (lower, higher) timeslice More...
enum class	EdgeType { SPACELIKE , TIMELIKE }
	Causal classification of an edge by its endpoint timeslices. More...
enum class	MoveRunCadenceError { NONPOSITIVE_PASSES , NONPOSITIVE_CHECKPOINT }
	Reasons raw move-run cadence cannot become a domain value. More...
enum class	MoveStrategyKind { MOVE_ALWAYS , METROPOLIS }
	The algorithms available to make ergodic moves on triangulations. More...
enum class	Topology { TOROIDAL , SPHERICAL }
	Spatial-topology label stored by configuration and persistence APIs. More...

Functions
template<typename ManifoldType, typename FunctionType, typename... Arguments>
constexpr auto	apply_move (ManifoldType const &t_manifold, FunctionType t_move, Arguments &&... arguments) -> decltype(auto)
	An applicative function similar to std::apply on a manifold.
constexpr auto	format_as (RandomSeed const seed) noexcept -> std::uint64_t
constexpr auto	format_as (RandomStream const stream) noexcept -> std::uint64_t
auto	operator<< (std::ostream &output, RandomSeed const seed) -> std::ostream &
auto	operator<< (std::ostream &output, RandomStream const stream) -> std::ostream &
auto	operator<< (std::ostream &t_os, Topology const &t_topology) -> std::ostream &
	Convert Topology to string output.

Variables
constexpr int	ALIGNMENT_32_BIT = 32
	Except when we only need 32 bits.
constexpr int	ALIGNMENT_64_BIT = 64
	Aligns data for ease of access on 64-bit CPUs at the expense of padding.
constexpr double	FOLIATION_SPACING = 1.0
	Default distance between successive foliated timeslices.
constexpr Int_precision	GV_BOUNDING_BOX_SIZE = 100
	Depends on INITIAL_RADIUS and RADIAL_FACTOR.
constexpr double	INITIAL_RADIUS = 1.0
	Default initial radius for generated foliated triangulations.
constexpr Int_precision	PRECISION = 256
	Sets the precision for MPFR.
constexpr double	TOLERANCE = 0.01
	Sets epsilon values for floating point comparisons.

Detailed Description

clang-15 does not support std::format

Typedef Documentation

◆ Causal_vertices_t

template<int dimension>

using cdt::Causal_vertices_t

Initial value:

std::vector<std::pair<Point_t<dimension>, Int_precision>>

cdt::Int_precision

std::int32_t Int_precision

Definition Settings.hpp:30

Point/time-label pairs used to build a causal triangulation.

Template Parameters

dimension Compile-time point dimension.

Definition at line 67 of file Foliated_triangulation.hpp.

◆ Cell_handle_t

template<int dimension>

using cdt::Cell_handle_t

Initial value:

typename detail::TriangulationTraits<dimension>::Cell_handle

Mutable CGAL cell handle for a triangulation dimension.

A handle borrows from the triangulation that produced it. It must not be used with a copy or after an invalidating mutation of its owner.

Template Parameters

dimension Compile-time triangulation dimension.

Definition at line 75 of file Foliated_triangulation.hpp.

◆ Delaunay_t

template<int dimension>

using cdt::Delaunay_t = typename detail::TriangulationTraits<dimension>::Delaunay

Delaunay triangulation type for dimension spatial dimensions.

Template Parameters

dimension Compile-time triangulation dimension.

Definition at line 57 of file Foliated_triangulation.hpp.

◆ Edge_handle_t

template<int dimension>

using cdt::Edge_handle_t

Initial value:

typename detail::TriangulationTraits<dimension>::Edge_handle

CGAL edge descriptor for a triangulation dimension.

The embedded cell handle borrows from its source triangulation and follows that triangulation's invalidation rules.

Template Parameters

dimension Compile-time triangulation dimension.

Definition at line 90 of file Foliated_triangulation.hpp.

◆ Facet_t

template<int dimension>

using cdt::Facet_t = typename detail::TriangulationTraits<dimension>::Facet

CGAL facet descriptor for a triangulation dimension.

The embedded cell handle borrows from its source triangulation and follows that triangulation's invalidation rules.

Template Parameters

dimension Compile-time triangulation dimension.

Definition at line 83 of file Foliated_triangulation.hpp.

◆ Geometry_3

using cdt::Geometry_3 = Geometry<3>

Three-dimensional simplex-count geometry.

Definition at line 113 of file Geometry.hpp.

◆ Gmpzf

using cdt::Gmpzf = CGAL::Gmpzf

Results are converted to a CGAL multi-precision floating point number. Gmpzf itself is based on GMP (https://gmplib.org), as is MPFR.

Definition at line 23 of file Settings.hpp.

◆ Int_precision

using cdt::Int_precision = std::int32_t

Sets the type of integer to use throughout the project. These are the base values read into the program or used in calculations. Casts to unsigned types are still necessary for certain library functions to work.

Definition at line 30 of file Settings.hpp.

◆ Metropolis_3

using cdt::Metropolis_3

Initial value:

MoveStrategy<MoveStrategyKind::METROPOLIS, manifolds::Manifold_3>

cdt::MoveStrategy

Select a move algorithm.

Definition Move_strategy.hpp:33

Metropolis-Hastings move strategy for the supported 3D manifold.

Definition at line 722 of file Metropolis.hpp.

◆ MoveAlways_3

using cdt::MoveAlways_3

Initial value:

MoveStrategy<MoveStrategyKind::MOVE_ALWAYS, manifolds::Manifold_3>

Always-accept-applicable move strategy for the supported 3D manifold.

Definition at line 212 of file Move_always.hpp.

◆ Point_t

template<int dimension>

using cdt::Point_t = typename detail::TriangulationTraits<dimension>::Point

Cartesian point type used by a triangulation dimension.

Template Parameters

dimension Compile-time triangulation dimension.

Definition at line 62 of file Foliated_triangulation.hpp.

◆ Spherical_points_generator_t

template<int dimension>

using cdt::Spherical_points_generator_t

Initial value:

typename detail::TriangulationTraits<

dimension>::Spherical_points_generator

CGAL random point generator on a sphere of matching dimension.

Template Parameters

dimension Compile-time point dimension.

Definition at line 104 of file Foliated_triangulation.hpp.

◆ Vertex_handle_t

template<int dimension>

using cdt::Vertex_handle_t

Initial value:

typename detail::TriangulationTraits<dimension>::Vertex_handle

Mutable CGAL vertex handle for a triangulation dimension.

A handle borrows from the triangulation that produced it. It must not be used with a copy or after an invalidating mutation of its owner.

Template Parameters

dimension Compile-time triangulation dimension.

Definition at line 98 of file Foliated_triangulation.hpp.

Enumeration Type Documentation

◆ CellType

enum class cdt::CellType

strong

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

Enumerator
THREE_ONE	Three lower-slice and one upper-slice vertices.
TWO_TWO	Two vertices on each adjacent slice.
ONE_THREE	One lower-slice and three upper-slice vertices.
ACAUSAL	Vertex times differ by more than one or are all equal.
UNCLASSIFIED	Classification could not determine a causal type.

Definition at line 352 of file Foliated_triangulation.hpp.

◆ EdgeType

enum class cdt::EdgeType

strong

Causal classification of an edge by its endpoint timeslices.

Enumerator
SPACELIKE	Both endpoints lie on the same timeslice.
TIMELIKE	Endpoints lie on adjacent timeslices.

Definition at line 363 of file Foliated_triangulation.hpp.

◆ MoveRunCadenceError

enum class cdt::MoveRunCadenceError

strong

Reasons raw move-run cadence cannot become a domain value.

Enumerator
NONPOSITIVE_PASSES	The requested pass count is not positive.
NONPOSITIVE_CHECKPOINT	The checkpoint interval is not positive.

Definition at line 27 of file Move_run.hpp.

◆ MoveStrategyKind

enum class cdt::MoveStrategyKind

strong

The algorithms available to make ergodic moves on triangulations.

Enumerator
MOVE_ALWAYS	Execute every applicable proposal.
METROPOLIS	Apply Metropolis-Hastings acceptance.

Definition at line 21 of file Move_strategy.hpp.

◆ Topology

enum class cdt::Topology

strong

Spatial-topology label stored by configuration and persistence APIs.

Enumerator
TOROIDAL	Reserved for toroidal slices; construction is unsupported.
SPHERICAL	Supported spherical spatial slices.

Definition at line 71 of file Utilities.hpp.

Function Documentation

◆ apply_move()

template<typename ManifoldType, typename FunctionType, typename... Arguments>

auto cdt::apply_move	(	ManifoldType const &	t_manifold,
		FunctionType	t_move,
		Arguments &&...	arguments ) -> decltype(auto)

nodiscardconstexpr

An applicative function similar to std::apply on a manifold.

Template Parameters

ManifoldType	The type (topology, dimensionality) of manifold
FunctionType	The type of move applied to the manifold

Parameters

t_manifold	The manifold on which to make the Pachner move
t_move	The Pachner move
arguments	Explicit dependencies forwarded to the move

Returns: The expected or unexpected result in a std::expected<T,E>

Definition at line 29 of file Apply_move.hpp.

◆ format_as() [1/2]

auto cdt::format_as ( RandomSeed const seed ) -> std::uint64_t

nodiscardconstexprnoexcept

Parameters

seed	Seed to expose to fmt-compatible formatting.

Returns: The seed's unsigned representation.

Definition at line 69 of file Random.hpp.

◆ format_as() [2/2]

auto cdt::format_as ( RandomStream const stream ) -> std::uint64_t

nodiscardconstexprnoexcept

Parameters

stream Stream selector to expose to fmt-compatible formatting.

Returns: The selector's unsigned representation.

Definition at line 75 of file Random.hpp.

◆ operator<<() [1/3]

auto cdt::operator<<	(	std::ostream &	output,
		RandomSeed const	seed ) -> std::ostream &

inline

Parameters

output	Destination stream.
seed	Seed to write as an unsigned integer.

Returns: output after insertion.

Definition at line 82 of file Random.hpp.

◆ operator<<() [2/3]

auto cdt::operator<<	(	std::ostream &	output,
		RandomStream const	stream ) -> std::ostream &

inline

Parameters

output	Destination stream.
stream	Stream selector to write as an unsigned integer.

Returns: output after insertion.

Definition at line 89 of file Random.hpp.

◆ operator<<() [3/3]

auto cdt::operator<<	(	std::ostream &	t_os,
		Topology const &	t_topology ) -> std::ostream &

inline

Convert Topology to string output.

Parameters

t_os	The output stream
t_topology	The topology

Returns: An output string of the topology

Definition at line 81 of file Utilities.hpp.

References SPHERICAL, and TOROIDAL.

Variable Documentation

◆ ALIGNMENT_32_BIT

int cdt::ALIGNMENT_32_BIT = 32

inlineconstexpr

Except when we only need 32 bits.

Definition at line 61 of file Settings.hpp.

◆ ALIGNMENT_64_BIT

int cdt::ALIGNMENT_64_BIT = 64

inlineconstexpr

Aligns data for ease of access on 64-bit CPUs at the expense of padding.

Definition at line 58 of file Settings.hpp.

◆ FOLIATION_SPACING

double cdt::FOLIATION_SPACING = 1.0

inlineconstexpr

Default distance between successive foliated timeslices.

Definition at line 49 of file Settings.hpp.

Referenced by cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::manifolds::Manifold< 3 >::Manifold(), cdt::manifolds::Manifold< 3 >::Manifold(), and cdt::manifolds::Manifold< 3 >::Manifold().

◆ GV_BOUNDING_BOX_SIZE

Int_precision cdt::GV_BOUNDING_BOX_SIZE = 100

inlineconstexpr

Depends on INITIAL_RADIUS and RADIAL_FACTOR.

Definition at line 55 of file Settings.hpp.

◆ INITIAL_RADIUS

double cdt::INITIAL_RADIUS = 1.0

inlineconstexpr

Default initial radius for generated foliated triangulations.

Definition at line 47 of file Settings.hpp.

Referenced by cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::foliated_triangulations::FoliatedTriangulation< 3 >::FoliatedTriangulation(), cdt::manifolds::Manifold< 3 >::Manifold(), cdt::manifolds::Manifold< 3 >::Manifold(), and cdt::manifolds::Manifold< 3 >::Manifold().

◆ PRECISION

Int_precision cdt::PRECISION = 256

inlineconstexpr

Sets the precision for MPFR.

Correctly declare global constants See Jonathan Boccara's C++ Pitfalls, January 2021

Definition at line 44 of file Settings.hpp.

◆ TOLERANCE

double cdt::TOLERANCE = 0.01

inlineconstexpr

Sets epsilon values for floating point comparisons.

Definition at line 52 of file Settings.hpp.

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

Namespaces

Classes

Concepts

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ Causal_vertices_t

◆ Cell_handle_t

◆ Delaunay_t

◆ Edge_handle_t

◆ Facet_t

◆ Geometry_3

◆ Gmpzf

◆ Int_precision

◆ Metropolis_3

◆ MoveAlways_3

◆ Point_t

◆ Spherical_points_generator_t

◆ Vertex_handle_t

Enumeration Type Documentation

◆ CellType

◆ EdgeType

◆ MoveRunCadenceError

◆ MoveStrategyKind

◆ Topology

Function Documentation

◆ apply_move()

◆ format_as() [1/2]

◆ format_as() [2/2]

◆ operator<<() [1/3]

◆ operator<<() [2/3]

◆ operator<<() [3/3]

Variable Documentation

◆ ALIGNMENT_32_BIT

◆ ALIGNMENT_64_BIT

◆ FOLIATION_SPACING

◆ GV_BOUNDING_BOX_SIZE

◆ INITIAL_RADIUS

◆ PRECISION

◆ TOLERANCE