C++ code for CGAL issue 8359

8358.cpp

#include <CGAL/Homogeneous.h>
#include <CGAL/Width_default_traits_3.h>
#include <CGAL/Width_3.h>

#include <iostream>
#include <cassert>
#include <vector>

typedef CGAL::Gmpz                            _RT;

typedef CGAL::Homogeneous<_RT>                _Kernel;
typedef _Kernel::Point_3                      _Point_3;
typedef _Kernel::Vector_3                     _Vector_3;
typedef _Kernel::Plane_3                      _Plane_3;
typedef CGAL::Width_default_traits_3<_Kernel> _Width_traits;
typedef CGAL::Width_3<_Width_traits>          _Width;

void print_vec(const std::vector<_Vector_3>& vec)
{
  for (std::vector<_Vector_3>::const_iterator it = vec.begin();
       it != vec.end(); ++ it)
    std::cerr << *it << std::endl;
}

std::vector<_Point_3> one = {{1, 0, 0}, {2, -1, 0}, {2, 0, -1}, {3, 0, 0}, {2, 1, 0}, {2, 0, 1}};

std::vector<_Point_3> two = {{725, -65, -11}, {736, -66, -11}, {336, -30, -5}, {347, -31, -5}, {1225, -110, -19}, {1269, -114, -19}, {-331, 30, 5}, {-287, 26, 5}, {1747, -157, -27}, {947, -85, -15}, {1780, -160, -27}, {-220, 20, 3}, {1024, -92, -15}, {-976, 88, 15}, {-143, 13, 3}, {-943, 85, 15}, {1869, -168, -29}, {1069, -96, -17}, {1913, -172, -29}, {-487, 44, 7}, {1157, -104, -17}, {-1243, 112, 19}, {-399, 36, 7}, {-1199, 108, 19}, {1591, -143, -25}, {1668, -150, -25}, {-1132, 102, 17}, {-1055, 95, 17}, {2268, -204, -35}, {268, -24, -5}, {2279, -205, -35}, {-121, 11, 1}, {389, -35, -5}, {-2011, 181, 31}, {0, 0, 1}, {-2000, 180, 31}, {1579, -142, -25}, {1667, -150, -25}, {-1533, 138, 23}, {-1445, 130, 23}, {1712, -154, -27}, {1312, -118, -21}, {2123, -191, -33}, {523, -47, -9}, {2156, -194, -33}, {-644, 58, 9}, {1789, -161, -27}, {-1411, 127, 21}, {1411, -127, -21}, {-1789, 161, 27}, {644, -58, -9}, {-2156, 194, 33}, {-523, 47, 9}, {-2123, 191, 33}, {-1312, 118, 21}, {-1712, 154, 27}, {1445, -130, -23}, {1533, -138, -23}, {-1667, 150, 25}, {-1579, 142, 25}, {2000, -180, -31}, {0, 0, -1}, {2011, -181, -31}, {-389, 35, 5}, {121, -11, -1}, {-2279, 205, 35}, {-268, 24, 5}, {-2268, 204, 35}, {1055, -95, -17}, {1132, -102, -17}, {-1668, 150, 25}, {-1591, 143, 25}, {1199, -108, -19}, {399, -36, -7}, {1243, -112, -19}, {-1157, 104, 17}, {487, -44, -7}, {-1913, 172, 29}, {-1069, 96, 17}, {-1869, 168, 29}, {943, -85, -15}, {143, -13, -3}, {976, -88, -15}, {-1024, 92, 15}, {220, -20, -3}, {-1780, 160, 27}, {-947, 85, 15}, {-1747, 157, 27}, {287, -26, -5}, {331, -30, -5}, {-1269, 114, 19}, {-1225, 110, 19}, {-347, 31, 5}, {-336, 30, 5}, {-736, 66, 11}, {-725, 65, 11}};

void demo(std::vector<_Point_3>& pts) {
    _Width _simplex(pts.begin(), pts.end());

    std::vector<_Vector_3> _dir;

    _simplex.get_all_build_directions(_dir);

    std::cerr << "opt: " << _simplex.get_number_of_optimal_solutions()
              << " (should be "
              << (pts.size()==6 ? 4 : 1) << ")" << std::endl;

    // workaround
    for (std::vector<_Vector_3>::iterator it = _dir.begin();
        it != _dir.end(); ++ it)
	    if (it->hx()<0 || (it->hx()==0 && it->hy()<0)
	                   || (it->hx()==0 && it->hy()==0 && it->hz()<0))
                *it = - *it;

    struct
    {
        bool operator()(_Vector_3 a, _Vector_3 b) const {
            if (a.hx() != b.hx())  return a.hx() < b.hx();
            if (a.hy() != b.hy())  return a.hy() < b.hy();
            return a.hz() < b.hz();
        }
    }
    customLess;

    struct
    {
        bool operator()(_Vector_3 a, _Vector_3 b) const {
            return a.hx()==b.hx() && a.hy()==b.hy() && a.hz()==b.hz();
        }
    }
    customEqual;

    std::sort(_dir.begin(), _dir.end(), customLess);

    std::vector<_Vector_3> res(_dir.begin(),
        std::unique(_dir.begin(), _dir.end(), customEqual));

    print_vec(res);
    std::cerr << std::endl;
}

int main() {
    demo(one);
    demo(two);

    return 0;
}

For CGAL/cgal#8358

$ g++ 8358.cpp -lgmp
$ ./a.out 
opt: 8 (should be 4)
4096 4096 4096 1
4096 -4096 4096 1
-4096 -4096 4096 1
-4096 4096 4096 1
-4096 4096 -4096 1
4096 4096 -4096 1
4096 -4096 -4096 1
-4096 -4096 -4096 1

opt: 8 (should be 1)
81920 917504 -40960 1
204800 2293760 -102400 1
122880 1376256 -61440 1
81920 917504 -40960 1
-122880 -1376256 61440 1
-40960 -458752 20480 1
-163840 -1835008 81920 1
-163840 -1835008 81920 1

$ 

I learned from Andreas to use "-DSIMPLIFY" while compiling.
Better, but still wrong, see argumentation here:
CGAL/cgal#8358 (comment)

pi@raspberrypi5:~/cgal4gp $ g++ -DSIMPLIFY 8358.cpp -lgmp 2>err
pi@raspberrypi5:~/cgal4gp $ ./a.out 
opt: 8 (should be 4)
1 1 1 1
1 -1 1 1
-1 -1 1 1
-1 1 1 1
-1 1 -1 1
1 1 -1 1
1 -1 -1 1
-1 -1 -1 1

opt: 8 (should be 1)
10 112 -5 1
10 112 -5 1
10 112 -5 1
10 112 -5 1
-10 -112 5 1
-10 -112 5 1
-10 -112 5 1
-10 -112 5 1

pi@raspberrypi5:~/cgal4gp $ 

"normalizing" works, need to figure out how to std::sort() std::vector<Vector_3> (std::vector<Point_3> is easy) as workaround, followed by std::unique():

hermann@7950x:~$ g++ -DSIMPLIFY 8358.cpp -lgmp
hermann@7950x:~$ ./a.out 
opt: 8 (should be 4)
1 1 1 1
1 -1 1 1
1 1 -1 1
1 -1 -1 1
1 -1 1 1
1 1 -1 1
1 -1 -1 1
1 1 1 1

opt: 8 (should be 1)
10 112 -5 1
10 112 -5 1
10 112 -5 1
10 112 -5 1
10 112 -5 1
10 112 -5 1
10 112 -5 1
10 112 -5 1

hermann@7950x:~$ 

Got it working with latest revision:

hermann@7950x:~$ g++ -DSIMPLIFY 8358.cpp -lgmp
hermann@7950x:~$ ./a.out 
opt: 8 (should be 4)
1 -1 -1 1
1 -1 1 1
1 1 -1 1
1 1 1 1

opt: 8 (should be 1)
10 112 -5 1

hermann@7950x:~$