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

CGAL 4.8 - Linear and Quadratic Programming Solver

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QP_solver/important_variables.cpp
// Example: find the points that contribute to a convex combination
#include <cassert>
#include <vector>
#include <CGAL/Cartesian_d.h>
#include <CGAL/MP_Float.h>
#include "solve_convex_hull_containment_lp2.h"
typedef CGAL::Cartesian_d<double> Kernel_d;
typedef Kernel_d::Point_d Point_d;
typedef CGAL::Quadratic_program_solution<CGAL::MP_Float> Solution;
int main()
{
std::vector<Point_d> points;
// convex hull: 4-gon spanned by {(1,0), (4,1), (4,4), (2,3)}
points.push_back (Point_d (1, 0)); // point 0
points.push_back (Point_d (4, 1)); // point 1
points.push_back (Point_d (4, 4)); // point 2
points.push_back (Point_d (2, 3)); // point 3
// test all 25 integer points in [0,4]^2
for (int i=0; i<=4; ++i)
for (int j=0; j<=4; ++j) {
Point_d p (i, j);
Solution s = solve_convex_hull_containment_lp
(p, points.begin(), points.end(), CGAL::MP_Float());
std::cout << p;
if (s.is_infeasible())
std::cout << " is not in the convex hull\n";
else {
assert (s.is_optimal());
std::cout << " is a convex combination of the points ";
Solution::Index_iterator it = s.basic_variable_indices_begin();
Solution::Index_iterator end = s.basic_variable_indices_end();
for (; it != end; ++it) std::cout << *it << " ";
std::cout << std::endl;
}
}
return 0;
}