\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 3D Periodic Triangulations
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Periodic_3_triangulation_3/covering.cpp
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Periodic_3_triangulation_traits_3.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
#include <iostream>
#include <vector>
typedef PDT::Point Point;
typedef PDT::Covering_sheets Covering_sheets;
int main()
{
PDT T;
// Input point grid (27 points)
for (double x=0. ; x < .9 ; x += 0.33) {
for (double y=0. ; y < .9 ; y += 0.33) {
for (double z=0. ; z < .9 ; z += 0.33) {
T.insert(Point(x,y,z));
} } }
Covering_sheets cs = T.number_of_sheets();
std::cout<<"Current covering: "<<cs[0]<<' '<<cs[1]<<' '<<cs[2]<<std::endl;
if ( T.is_triangulation_in_1_sheet() ) { // = true
bool is_extensible = T.is_extensible_triangulation_in_1_sheet_h1()
|| T.is_extensible_triangulation_in_1_sheet_h2(); // = false
T.convert_to_1_sheeted_covering();
cs = T.number_of_sheets();
std::cout<<"Current covering: "<<cs[0]<<' '<<cs[1]<<' '<<cs[2]<<std::endl;
if ( is_extensible ) // = false
std::cout<<"It is safe to change the triangulation here."<<std::endl;
else
std::cout<<"It is NOT safe to change the triangulation here!"<<std::endl;
T.convert_to_27_sheeted_covering();
cs = T.number_of_sheets();
std::cout<<"Current covering: "<<cs[0]<<' '<<cs[1]<<' '<<cs[2]<<std::endl;
}
std::cout<<"It is (again) safe to modify the triangulation."<<std::endl;
return 0;
}