CGAL 5.6.3 - Optimal Distances

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Polytope_distance_d/polytope_distance_d.cpp
// computes the distance between two cubes in R^3 using double
// as input type and some internal EXACT floating point type
#include <CGAL/Polytope_distance_d.h>
#include <CGAL/Polytope_distance_d_traits_3.h>
#include <CGAL/Homogeneous.h>
#include <iostream>
#include <cassert>
#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 EXACT kernel...
typedef CGAL::Homogeneous<ET> K;
typedef K::Point_3 Point;
// ...and the traits class based on the exact kernel
typedef CGAL::Polytope_distance_d_traits_3<K> 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;
}
CGAL::Polytope_distance_d_traits_3
The class Polytope_distance_d_traits_3 is a traits class for the -dimensional optimisation algorithms...
Definition: Polytope_distance_d_traits_3.h:25
CGAL::Polytope_distance_d
An object of the class Polytope_distance_d represents the (squared) distance between two convex polyt...
Definition: Polytope_distance_d.h:58
CGAL::to_double
double to_double(const NT &x)
CGAL::Homogeneous