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

CGAL 4.8 - Optimal Distances

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Polytope_distance_d/polytope_distance_d_fast_exact.cpp
// computes the distance between two cubes in R^3 using double
// as input type and some internal EXACT floating point type;
// the fast type double is also safely used for many of the
// internal computations
#include <iostream>
#include <cassert>
#include <CGAL/Homogeneous.h>
#include <CGAL/Polytope_distance_d.h>
#include <CGAL/Polytope_distance_d_traits_3.h>
#ifdef CGAL_USE_GMP
#include <CGAL/Gmpzf.h>
typedef CGAL::Gmpzf ET;
#else
#include <CGAL/MP_Float.h>
typedef CGAL::MP_Float ET;
#endif
// use an inexact kernel...
typedef CGAL::Homogeneous<double> K;
typedef K::Point_3 Point;
// ... and the EXACT traits class based on the inexcat kernel
typedef CGAL::Polytope_distance_d_traits_3<K, ET, double> Traits;
typedef CGAL::Polytope_distance_d<Traits> Polytope_distance;
int main()
{
// the cube [0,1]^3
Point P[8] = { Point(0,0,0), Point(0,0,1), Point(0,1,0), Point(0,1,1),
Point(1,0,0), Point(1,0,1), Point(1,1,0), Point(1,1,1)};
// the cube [2,3]^3
Point Q[8] = { Point(2,2,2), Point(2,2,3), Point(2,3,2), Point(2,3,3),
Point(3,2,2), Point(3,2,3), Point(3,3,2), Point(3,3,3)};
Polytope_distance pd(P, P+8, Q, Q+8);
assert (pd.is_valid());
// get squared distance (2,2,2)-(1,1,1))^2 = 3
std::cout << "Squared distance: " <<
CGAL::to_double (pd.squared_distance_numerator()) /
CGAL::to_double (pd.squared_distance_denominator()) << std::endl;
// get points that realize the distance
Polytope_distance::Coordinate_iterator coord_it;
std::cout << "p:"; // homogeneous point from first cube, (1,1,1,1)
for (coord_it = pd.realizing_point_p_coordinates_begin();
coord_it != pd.realizing_point_p_coordinates_end();
++coord_it)
std::cout << " " << *coord_it;
std::cout << std::endl;
std::cout << "q:"; // homogeneous point from second cube, (2,2,2,1)
for (coord_it = pd.realizing_point_q_coordinates_begin();
coord_it != pd.realizing_point_q_coordinates_end();
++coord_it)
std::cout << " " << *coord_it;
std::cout << std::endl;
return 0;
}