CGAL 4.7 - Optimal Distances: Polytope_distance_d/width_simplex.cpp

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - Optimal Distances

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Polytope_distance_d/width_simplex.cpp
#include <CGAL/Homogeneous.h>
#include <CGAL/Width_default_traits_3.h>
#include <CGAL/Width_3.h>
#include <iostream>
#include <vector>
#if defined(CGAL_USE_GMP)
#include <CGAL/Gmpz.h>
typedef CGAL::Gmpz RT;
#elif defined (CGAL_USE_LEDA)
#include <CGAL/leda_integer.h>
typedef leda_integer RT;
#else
#include <CGAL/MP_Float.h>
typedef CGAL::MP_Float RT;
#endif
typedef CGAL::Homogeneous<RT> Kernel;
typedef Kernel::Point_3 Point_3;
typedef Kernel::Plane_3 Plane_3;
typedef CGAL::Width_default_traits_3<Kernel> Width_traits;
typedef CGAL::Width_3<Width_traits> Width;
int main() {
// Create a simplex using homogeneous integer coordinates
std::vector<Point_3> points;
points.push_back( Point_3(2,0,0,1));
points.push_back( Point_3(0,1,0,1));
points.push_back( Point_3(0,0,1,1));
points.push_back( Point_3(0,0,0,1));
// Compute width of simplex
Width simplex( points.begin(), points.end());
// Output of squared width, width-planes, and optimal direction
RT wnum, wdenom;
simplex.get_squared_width( wnum, wdenom);
std::cout << "Squared Width: " << wnum << "/" << wdenom << std::endl;
std::cout << "Direction: " << simplex.get_build_direction() << std::endl;
Plane_3 e1, e2;
simplex.get_width_planes (e1, e2);
std::cout << "Planes: E1: " << e1 << ". E2: " << e2 <<std::endl;
std::cout << "Number of optimal solutions: "
<< simplex.get_number_of_optimal_solutions() << std::endl;
return(0);
}