How to do Ray and Triangle Edge intersect?

Question

I'm facing problem intersecting ray with triangle edges. Actually, I'm trying to pick/intersect with triangle, vertex, edge of a mesh using Mouse. So I made ray from the Mouse current position and then I intersect it with the mesh elements like triangle/polygon, vertex, edge etc to work with it. Basically, 3d modeling stuffs. Intersecting with triangle was easy and fun. And the vertex part was tricky.

But now, I don't know how to intersect/pick with triangle edges. I mean how I treat them when intersecting with the Mouse Ray? First I thought they can be treated like a 3D line. But eventually failed to do the Ray and the Line intersect. Searched on the Internet but not found any helpful info. Although I found some open source projects are using OpenGL built-in picking features to pick/intersect with Edge. But in my case, I can't use that. :(

My current edge picking code structure looks like the following:

void pickEdge(Ray ray, Scene scene)
{
    for each object in scene
    {
        mesh = getMesh(object)
        for each triangle in mesh
        {
            for each edge in triangle
            {
                v1 = getV1(edge)
                v2 = getV2(edge)

                // Do intersect with 'ray' and 'v1', 'v2'. But how?
            }
        }
    }
}

So I'm stuck here and really need some help. Any idea, algorithm or a small help is greatly appreciated.

Answer 1

In your case problem of finding intersection between triangle and ray in 3D space can be boiled down to finding point location (INSIDE, OUTSIDE, ON BOUNDARY) in triangle in 2D space (plane). All you should do is project triangle on screen plane, find intersection on edge and perform reverse projection on edge. Position of point is position of mouse. The only problem is to treat degenerate cases like mapping triangle into line segment. But I think it will not be problem, because such cases can be easily coped.