int intersec(const line& l1, const line& l2,
point& res){
assert(!(l1.v == point()));
assert(!(l2.v == point()));
if (vp(l1.v,l2.v) == point()){
if (vp(l1.v, l1.p - l2.p) == point())
return 2; // same
return 0; // parallel
}
point n = vp(l1.v,l2.v);
point p = l2.p - l1.p;
if (sgn(sp(n,p)))
return 0; // skew
ld t;
if (sgn(n.x))
t = (p.y * l2.v.z - p.z * l2.v.y) / n.x;
else if (sgn(n.y))
t = (p.z * l2.v.x - p.x * l2.v.z) / n.y;
else if (sgn(n.z))
t = (p.x * l2.v.y - p.y * l2.v.x) / n.z;
else
assert(false);
res = l1.p + l1.v * t;
assert(l1.on(res)); assert(l2.on(res));
return 1; // intersects
}
void closest(const line& l1,const line& l2,
point& p1,point& p2){
if (vp(l1.v,l2.v) == point()){
p1 = l1.p;
p2 = l2.p - l1.v * /*BOXNEXT*/
(sp(l1.v,l2.p - l1.p) / l1.v.dist2());
return;
}
point p = l2.p - l1.p;
ld t1 = (
sp(l1.v,p) * l2.v.dist2() -
sp(l1.v,l2.v) * sp(l2.v,p)
) / vp(l1.v,l2.v).dist2();
ld t2 = (
sp(l2.v,l1.v) * sp(l1.v,p) -
sp(l2.v,p) * l1.v.dist2()
) / vp(l2.v,l1.v).dist2();
p1 = l1.p + l1.v * t1;
p2 = l2.p + l2.v * t2;
assert(l1.on(p1));
assert(l2.on(p2));
}
bool cross( line L ) { return on( intersect( L ) ) && L.on( intersect( L ) ); }