Möller-Trumbore intersection point

Question

I am using the Möller-Trumbore method as part of my (still very basic) collision detection system.

The information I'm craving about is the distance from the ray origin and intersection point. The intersection point would be fine too obviously.

I probably wrongly assumed t in the code below is actually the distance from the ray origin to the intersection point. If it actually is, then I don't know what's wrong with my code.

I have got a simulation with a mesh and "bullets", sometimes firing a collision acurately, and sometimes not (bullets passing thru mesh, or firing a colision before it actually should hit).

bool rayTriangleIntersect(const XMFLOAT3 &orig, const XMFLOAT3 &dir, const XMFLOAT3 &v0, const XMFLOAT3 &v1, const XMFLOAT3 &v2, float &t, float &u, float &v) {
// http://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/moller-trumbore-ray-triangle-intersection

    float kEpsilon = 0.000001f;
    XMFLOAT3 v0v1 = v1 - v0;
    XMFLOAT3 v0v2 = v2 - v0;
    XMFLOAT3 pvec = XMFLOAT3Cross(dir, v0v2);

    float det = XMFLOAT3Dot(v0v1, pvec);

    if (det < kEpsilon) return false;

    float invDet = 1.0f / det;

    XMFLOAT3 tvec = orig - v0;
    u = XMFLOAT3Dot(tvec, pvec) * invDet;
    if (u < 0 || u > 1) return false;

    XMFLOAT3 qvec = XMFLOAT3Cross(tvec, v0v1);
    v = XMFLOAT3Dot(dir, qvec) * invDet;
    if (v < 0 || u + v > 1) return false;

    t = XMFLOAT3Dot(v0v2, qvec) * invDet;

    return true;
}

Is t really the distance im looking for ? If not how do I get it, or the intersection point. I've heard of baricentric coordinates in a triangle related to u and v - is it the way to go ? If yes I'd be thankful for an example or link related to the Möller-Trumbore method.

Thanks!

Answer 1

One issue with your implementation is that you only check if det is smaller kEpsilon, but there is no guarantee that det is positive. You want to check

if(det<kEpsilon && det>-kEpsilon)

So that might explain the false positives. The way this algorithm works is by basically figuring out "when" the ray will hit the triangles plane and then checking if the position of the ray at that time is inside the triangle by transforming into barycentric coordinates.

You should be able to calculate the intersection point as:

intersection = v0+u*v0v2+v*v0v1;

That being said t should be the distance you are looking for anyway, so you might have an implementation problem.

There seems to be an excellent explanation here: http://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/moller-trumbore-ray-triangle-intersection

Answer 2

A standard parametric ray equation is r(t) = p + td. The origin point is p and d is the ray direction. So, that algorithm gives you t and you know p and d already. Therefore you can compute ray (or vector) r(t), and then take its magnitude |r(t)| to obtain the distance to triangle (intersection).

PS. You may need to normalize your direction vector d first. That is, ensure its of unit length. (The link you provided isn't clear if that's necessary though.)