Function proper_intersection

Geometry/Geometry 3D.cpp:578–586

}

bool proper_intersection(p3 a, p3 b, p3 c, p3 d, p3 &out) {
    p3 ab = a * b, cd = c * d; // normals of planes OAB and OCD
    int oa = sign(cd | a),
        ob = sign(cd | b),
        oc = sign(ab | c),
        od = sign(ab | d);
    out = ab * cd * od; // four multiplications => careful with overflow!
    return (oa != ob && oc != od && oa != oc);
}

// Assume that the sphere is centered at the origin
bool point_on_sphere_segment(p3 a, p3 b, p3 p) {