/** The Triangle-Triangle test implementation is based on pseudo-code from Tomas Möller's
"A Fast Triangle-Triangle Intersection Test": http://jgt.akpeters.com/papers/Moller97/.
See also Christer Ericson's Real-Time Collision Detection, p. 172. */
bool Triangle::Intersects(const Triangle &t2, LineSegment *outLine) const
{
// Is the triangle t2 completely on one side of the plane of this triangle?
Plane p1 = this->PlaneCCW();
float t2da = p1.SignedDistance(t2.a);
float t2db = p1.SignedDistance(t2.b);
float t2dc = p1.SignedDistance(t2.c);
if (t2da*t2db > 0.f && t2da*t2dc > 0.f)
return false;
// Is this triangle completely on one side of the plane of the triangle t2?
Plane p2 = t2.PlaneCCW();
float t1da = p2.SignedDistance(this->a);
float t1db = p2.SignedDistance(this->b);
float t1dc = p2.SignedDistance(this->c);
if (t1da*t1db > 0.f && t1da*t1dc > 0.f)
return false;
// Find the intersection line of the two planes.
Line l;
bool success = p1.Intersects(p2, &l);
assume(success); // We already determined the two triangles have intersecting planes, so this should always succeed.
if (!success)
return false;
// Find the two line segments of both triangles which straddle the intersection line.
LineSegment l1a, l1b;
LineSegment l2a, l2b;
FindIntersectingLineSegments(*this, t1da, t1db, t1dc, l1a, l1b);
FindIntersectingLineSegments(t2, t2da, t2db, t2dc, l2a, l2b);
// Find the projection intervals on the intersection line.
float d1a, d1b, d2a, d2b;
l.Distance(l1a, &d1a);
l.Distance(l1b, &d1b);
l.Distance(l2a, &d2a);
l.Distance(l2b, &d2b);
if (d1a > d1b)
Swap(d1a, d1b);
if (d2a > d2b)
Swap(d2a, d2b);
float rStart = Max(d1a, d2a);
float rEnd = Min(d1b, d2b);
if (rStart <= rEnd)
{
if (outLine)
*outLine = LineSegment(l.GetPoint(rStart), l.GetPoint(rEnd));
return true;
}
return false;
}
