Pathtracing Ray Triangle Intersection

Question

I am currently writing a pathtracer. Now i want to implement ray - triangle intersection. So my triangle consists of three Points (v0,v1,v2). I looked at other posts on this topic (Raytracing - Ray/Triangle Intersection). Sadly it is not working correctly so i want to check if the problem is on the intersection side. Here are my two triangle functions:

public float intersect(Ray ray){
    Vector3D e1 = v1.sub(v0);
    Vector3D e2 = v2.sub(v0);
    Vector3D e1e2 = e1.cross(e2).normalize();

    Vector3D p = ray.direction.cross(e2);

    float a = e1.dot(p);
    if(a < 0.0)
        return -1.0f;

    float f = 1.0f / a;
    Vector3D s = ray.origin.sub(v0);
    float u = f*(s.dot(p));
    if(u < 0.0 || u > 1.0)
        return -1.0f; //no hit

    Vector3D q = s.cross(e1);
    float v = f * (ray.direction.dot(q));
    if(v < 0.0 || v > 1.0)
        return -1.0f; //no hit

    float t = f * (e2.dot(q)); //distance
    return t;
}

public Vector3D normal(Vector3D nVec){
    Vector3D e1 = v1.sub(v0);
    Vector3D e2 = v2.sub(v0);
    Vector3D e1e2 = e1.cross(e2).normalize();
    return e1e2;
}

So is this code correct?

Leah Lindner Leah Lindner · Accepted Answer · 2015-01-04T18:06:49

I honestly find your code rather hard to read because you don't use very descriptive names. I am going to give you what I did in pseudocode:

//1.Find intersection point of the ray and the infinite Plane created by triangle,
//or find if the ray is parralel to the plane (no intersection Point)
//2.Find out if the intersection point is within the triangle itself

Triangle: Vector A, Vector B, Vector C
ray: Vector rayOrig, Vector rayDir
Intersection: boolean hasHit = false, Vector hitPoint, float t

Vector normal = (B-A)CrossProduct(C-A) //I think you had basically the same with e1e2
float d = (normal)DotProduct(A)
float nd = (normal)DotProduct(rayDir)
if(nd!=0)
{    //The ray hits the triangles plane
    Intersection.t=(d- (normal).DotProduct(rayOrig))/nd
    Intersection.hitPoint=rayOrig+(rayDir*Intersection.t)
    if (pointInTriangle(Intersection.hitPoint, A, B, C))
    {
         Intersection.hasHit = true
    }
}
return Intersection

Notice that after getting the intersection point with the plane the function point in triangle is called, which should return a boolean. I got my method for that from: http://www.blackpawn.com/texts/pointinpoly/ using the second barycentric coordiantes, it looks like you are doing something similar in this part

if(u < 0.0 || u > 1.0)
    return -1.0f; //no hit

Vector3D q = s.cross(e1);
float v = f * (ray.direction.dot(q));
if(v < 0.0 || v > 1.0)
    return -1.0f; //no hit

It doesnt look like you are checking for ray plane intersection at all though, are you doing that in a different function? If that is the case, I dont think you actually need the rays direction for a triangle test.

Pathtracing Ray Triangle Intersection

2 Answers