std::size_t hash_value(const CGAL::Segment_3<Kernel>& segment)
{
std::size_t seed = 0;
boost::hash_combine(seed, segment.source());
boost::hash_combine(seed, segment.target());
return seed;
}
IGL_INLINE bool igl::copyleft::cgal::segment_segment_squared_distance(
const CGAL::Segment_3<Kernel> & S1,
const CGAL::Segment_3<Kernel> & S2,
CGAL::Point_3<Kernel> & P1,
CGAL::Point_3<Kernel> & P2,
typename Kernel::FT & dst)
{
typedef CGAL::Point_3<Kernel> Point_3;
typedef CGAL::Vector_3<Kernel> Vector_3;
typedef typename Kernel::FT EScalar;
if(S1.is_degenerate())
{
// All points on S1 are the same
P1 = S1.source();
point_segment_squared_distance(P1,S2,P2,dst);
return true;
}else if(S2.is_degenerate())
{
assert(!S1.is_degenerate());
// All points on S2 are the same
P2 = S2.source();
point_segment_squared_distance(P2,S1,P1,dst);
return true;
}
assert(!S1.is_degenerate());
assert(!S2.is_degenerate());
Vector_3 u = S1.target() - S1.source();
Vector_3 v = S2.target() - S2.source();
Vector_3 w = S1.source() - S2.source();
const auto a = u.dot(u); // always >= 0
const auto b = u.dot(v);
const auto c = v.dot(v); // always >= 0
const auto d = u.dot(w);
const auto e = v.dot(w);
const auto D = a*c - b*b; // always >= 0
assert(D>=0);
const auto sc=D, sN=D, sD = D; // sc = sN / sD, default sD = D >= 0
const auto tc=D, tN=D, tD = D; // tc = tN / tD, default tD = D >= 0
bool parallel = false;
// compute the line parameters of the two closest points
if (D==0)
{
// the lines are almost parallel
parallel = true;
sN = 0.0; // force using source point on segment S1
sD = 1.0; // to prevent possible division by 0.0 later
tN = e;
tD = c;
} else
{
// get the closest points on the infinite lines
sN = (b*e - c*d);
tN = (a*e - b*d);
if (sN < 0.0)
{
// sc < 0 => the s=0 edge is visible
sN = 0.0;
tN = e;
tD = c;
} else if (sN > sD)
{ // sc > 1 => the s=1 edge is visible
sN = sD;
tN = e + b;
tD = c;
}
}
if (tN < 0.0)
{
// tc < 0 => the t=0 edge is visible
tN = 0.0;
// recompute sc for this edge
if (-d < 0.0)
{
sN = 0.0;
}else if (-d > a)
{
sN = sD;
}else
{
sN = -d;
sD = a;
}
}else if (tN > tD)
{
// tc > 1 => the t=1 edge is visible
tN = tD;
// recompute sc for this edge
if ((-d + b) < 0.0)
{
sN = 0;
}else if ((-d + b) > a)
{
sN = sD;
}else
{
sN = (-d + b);
sD = a;
}
}
// finally do the division to get sc and tc
sc = (abs(sN) == 0 ? 0.0 : sN / sD);
tc = (abs(tN) == 0 ? 0.0 : tN / tD);
// get the difference of the two closest points
P1 = S1.source() + sc*(S1.target()-S1.source());
P2 = S2.source() + sc*(S2.target()-S2.source());
Vector_3 dP = w + (sc * u) - (tc * v); // = S1(sc) - S2(tc)
assert(dP == (P1-P2));
dst = dP.squared_length(); // return the closest distance
return parallel;
}