Ray-triangle intersection in C++

Question

I've been given some example code that I need to fix, and one function that I need to create will be used for triangle ray-tracing. I've currently got the code set up like this.

/*RayHitResult is a struct that determines if the ray has reached a polygon*/
RayHitResult TriangleIntersect(Ray& ray)
{
    RayHitResult result = Ray::s_defaultHitResult;
    double t = 10000; /*This is an extreme value for testing*/
    Vector3 point;
    Vector3 edge1 = m_vertices[1] - m_vertices[0]; /*m_vertices[0], [1] and [2] are the vertices of the triangle*/
    Vector3 edge2 = m_vertices[2] - m_vertices[0];
    Vector3 t_normal = edge1.CrossProduct(edge2); /*This is the normal*/
    double d = -(m_vertices[0].DotProduct(t_normal)); /*This is the offset*/

    t = -(ray.GetRayStart().DotProduct(t_normal) + d) / (ray.GetRay().DotProduct(t_normal)); /*The variable t is what I need to calculate*/

    point = ray.GetRayStart() + ray.GetRay()*t;

    /*This statement alters the result depending on whether there was an intersection*/
    if (t > 0 && t < 10000) 
    {
        result.t = t;
        result.normal = this->m_normal;
        result.point = point;
        result.data = this;
        return result;
    }

    return result;
}

I need to calculate the value of the variable "t" in order to determine whether the ray has intersected with a polygon. However, the current equation used to calculate "t" is incorrect as it does not produce a specified result. I've been told that the formula I'm using is correct, so can anyone tell me why the current "t" equation doesn't work?

enter image description here

n is the normal, d is the offset, S is the ray origin and v is the ray itself.

P i P i · Accepted Answer · 2015-01-23T14:56:39

I always find it easiest to derive these equations from scratch.

The triangle can be considered as an origin o and 2 vectors u and v.

o + au + bv specifies a plane.

So first you take your ray k+tl, and find the value of t where that ray intersects with that plane.

That appears to be what your code chunk is doing.

(Note that there is a very small chance the ray is flying parallel to the plane and no collision will occur; you will want to check your code handles potential div-by-0 gracefully)

Let's call this collision point s.

But the job is not yet done. The task is now to determine whether s is inside the triangle.

If you can express s as o + au + bv, then examining a and b will give you the answers.

And if a and b are BOTH between 0 and 1, then the point is within the parallelogram with origin o, and edges a and b.

Furthermore, if a+b < 1 the point is within it's lower TRIANGLE.

Ray-triangle intersection in C++

1 Answers