private static OrderedTriple LineLineIntersect(
OrderedTriple p1, OrderedTriple p2, OrderedTriple p3, OrderedTriple p4) {
double EPS = 1e-12;
OrderedTriple p13 = new OrderedTriple(),
p43 = new OrderedTriple(),
p21 = new OrderedTriple(),
pa = new OrderedTriple(),
pb = new OrderedTriple();
double d1343, d4321, d1321, d4343, d2121;
double numer, denom, mua, mub;
p13.x = p1.x - p3.x;
p13.y = p1.y - p3.y;
p13.z = p1.z - p3.z;
p43.x = p4.x - p3.x;
p43.y = p4.y - p3.y;
p43.z = p4.z - p3.z;
if (Math.abs(p43.x) < EPS && Math.abs(p43.y) < EPS && Math.abs(p43.z) < EPS) return (null);
p21.x = p2.x - p1.x;
p21.y = p2.y - p1.y;
p21.z = p2.z - p1.z;
if (Math.abs(p21.x) < EPS && Math.abs(p21.y) < EPS && Math.abs(p21.z) < EPS) return (null);
d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;
denom = d2121 * d4343 - d4321 * d4321;
if (Math.abs(denom) < EPS) return (null);
numer = d1343 * d4321 - d1321 * d4343;
mua = numer / denom;
mub = (d1343 + d4321 * (mua)) / d4343;
pa.x = p1.x + mua * p21.x;
pa.y = p1.y + mua * p21.y;
pa.z = p1.z + mua * p21.z;
pb.x = p3.x + mub * p43.x;
pb.y = p3.y + mub * p43.y;
pb.z = p3.z + mub * p43.z;
return pa.mid(pb);
}
