Periodic_3_triangulations.hpp File Reference

Toroidal 3D triangulations. More...

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
#include <CGAL/Periodic_3_triangulation_filtered_traits_3.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/Random.h>
#include <CGAL/Timer.h>
#include <CGAL/Triangulation_vertex_base_with_info_3.h>
#include <cassert>
#include <vector>

Include dependency graph for Periodic_3_triangulations.hpp:

Go to the source code of this file.

Typedefs
using	Cb = CGAL::Triangulation_cell_base_3< GT, CbDS >
using	CbDS = CGAL::Periodic_3_triangulation_ds_cell_base_3<>
using	GT = CGAL::Periodic_3_triangulation_filtered_traits_3< K >
using	K = CGAL::Exact_predicates_inexact_constructions_kernel
using	Kd = CGAL::Cartesian_d< double >
	Random point generators for d-dimensional points in a d-cube per timeslice.
using	PDT = CGAL::Periodic_3_Delaunay_triangulation_3< GT, TDS >
using	Point = Kd::Point_d
using	T3Point = PDT::Point
using	T3Vb = CGAL::Triangulation_vertex_base_3< GT, VbDS >
using	TDS = CGAL::Triangulation_data_structure_3< VbInfo, Cb >
using	VbDS = CGAL::Periodic_3_triangulation_ds_vertex_base_3<>
using	VbInfo = CGAL::Triangulation_vertex_base_with_info_3< int, GT, T3Vb >
	Allows each vertex to contain an integer denoting its timeslice.

Functions
template<typename T >
void	make_random_T3_triangulation (T *T3, int simplices, int timeslices) noexcept
	Make 3D toroidal (periodic) triangulations.

Detailed Description

Toroidal 3D triangulations.

Causal Dynamical Triangulations in C++ using CGAL

Copyright © 2014 Adam Getchell

Periodic (toroidal) 3D triangulations

Author

Adam Getchell

Definition in file Periodic_3_triangulations.hpp.

Typedef Documentation

Cb

using Cb = CGAL::Triangulation_cell_base_3<GT, CbDS>

Definition at line 32 of file Periodic_3_triangulations.hpp.

CbDS

using CbDS = CGAL::Periodic_3_triangulation_ds_cell_base_3<>

Definition at line 31 of file Periodic_3_triangulations.hpp.

GT

using GT = CGAL::Periodic_3_triangulation_filtered_traits_3<K>

Definition at line 26 of file Periodic_3_triangulations.hpp.

K

using K = CGAL::Exact_predicates_inexact_constructions_kernel

Definition at line 25 of file Periodic_3_triangulations.hpp.

Kd

using Kd = CGAL::Cartesian_d<double>

Random point generators for d-dimensional points in a d-cube per timeslice.

Definition at line 41 of file Periodic_3_triangulations.hpp.

PDT

using PDT = CGAL::Periodic_3_Delaunay_triangulation_3<GT, TDS>

Definition at line 37 of file Periodic_3_triangulations.hpp.

Point

typedef Point_t< 3 > Point

Initial value:

{
  spdlog::debug("3-Manifold validation and fixing.\n")

Definition at line 42 of file Periodic_3_triangulations.hpp.

T3Point

using T3Point = PDT::Point

Definition at line 38 of file Periodic_3_triangulations.hpp.

T3Vb

using T3Vb = CGAL::Triangulation_vertex_base_3<GT, VbDS>

Definition at line 29 of file Periodic_3_triangulations.hpp.

TDS

using TDS = CGAL::Triangulation_data_structure_3<VbInfo, Cb>

Definition at line 36 of file Periodic_3_triangulations.hpp.

VbDS

using VbDS = CGAL::Periodic_3_triangulation_ds_vertex_base_3<>

Definition at line 28 of file Periodic_3_triangulations.hpp.

VbInfo

using VbInfo = CGAL::Triangulation_vertex_base_with_info_3<int, GT, T3Vb>

Allows each vertex to contain an integer denoting its timeslice.

Definition at line 35 of file Periodic_3_triangulations.hpp.

Function Documentation

make_random_T3_triangulation()

template<typename T >

void make_random_T3_triangulation ( T *  T3, int  simplices, int  timeslices  )

noexcept

Make 3D toroidal (periodic) triangulations.

We can't directly pick number of simplices as we can in S3 but a point has <6 simplices in 3D

We're working on 2 dimensional random points with the z component fixed by the timeslice

In d-dimensions the range of points in a d-cube is the d-th root

Setup random point creation in a square (2-cube)

Debugging

Definition at line 46 of file Periodic_3_triangulations.hpp.