Möller–Trumbore intersection algorithm

The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle.[1] Among other uses, it can be used in computer graphics to implement ray tracing computations involving triangle meshes.[2]

C++ implementation

The following is an implementation of the algorithm in C++:

bool RayIntersectsTriangle(Vector3D rayOrigin, 
                           Vector3D rayVector, 
                           Triangle* inTriangle,
                           Vector3D& outIntersectionPoint)
{
    const float EPSILON = 0.0000001;
    Vector3D vertex0 = inTriangle->vertex0;
    Vector3D vertex1 = inTriangle->vertex1;  
    Vector3D vertex2 = inTriangle->vertex2;
    Vector3D edge1, edge2, h, s, q;
    float a,f,u,v;
    edge1 = vertex1 - vertex0;
    edge2 = vertex2 - vertex0;
    h = rayVector.crossProduct(edge2);
    a = edge1.dotProduct(h);
    if (a > -EPSILON && a < EPSILON)
        return false;    // This ray is parallel to this triangle.
    f = 1.0/a;
    s = rayOrigin - vertex0;
    u = f * s.dotProduct(h);
    if (u < 0.0 || u > 1.0)
        return false;
    q = s.crossProduct(edge1);
    v = f * rayVector.dotProduct(q);
    if (v < 0.0 || u + v > 1.0)
        return false;
    // At this stage we can compute t to find out where the intersection point is on the line.
    float t = f * edge2.dotProduct(q);
    if (t > EPSILON) // ray intersection
    {
        outIntersectionPoint = rayOrigin + rayVector * t;
        return true;
    }
    else // This means that there is a line intersection but not a ray intersection.
        return false;
}

Java implementation

The following is an implementation of the algorithm in Java using javax.vecmath from Java 3D API:

public class MollerTrumbore {

    private static final double EPSILON = 0.0000001;

    public static boolean rayIntersectsTriangle(Point3d rayOrigin, 
                                                Vector3d rayVector,
                                                Triangle inTriangle,
                                                Point3d outIntersectionPoint) {
        Point3d vertex0 = inTriangle.getVertex0();
        Point3d vertex1 = inTriangle.getVertex1();
        Point3d vertex2 = inTriangle.getVertex2();
        Vector3d edge1 = new Vector3d();
        Vector3d edge2 = new Vector3d();
        Vector3d h = new Vector3d();
        Vector3d s = new Vector3d();
        Vector3d q = new Vector3d();
        double a, f, u, v;
        edge1.sub(vertex1, vertex0);
        edge2.sub(vertex2, vertex0);
        h.cross(rayVector, edge2);
        a = edge1.dot(h);
        if (a > -EPSILON && a < EPSILON) {
            return false;    // This ray is parallel to this triangle.
        }
        f = 1.0 / a;
        s.sub(rayOrigin, vertex0);
        u = f * (s.dot(h));
        if (u < 0.0 || u > 1.0) {
            return false;
        }
        q.cross(s, edge1);
        v = f * rayVector.dot(q);
        if (v < 0.0 || u + v > 1.0) {
            return false;
        }
        // At this stage we can compute t to find out where the intersection point is on the line.
        double t = f * edge2.dot(q);
        if (t > EPSILON) // ray intersection
        {
            outIntersectionPoint.set(0.0, 0.0, 0.0);
            outIntersectionPoint.scaleAdd(t, rayVector, rayOrigin);
            return true;
        } else // This means that there is a line intersection but not a ray intersection.
        {
            return false;
        }
    }
}

See also

References
  1. Möller, Tomas; Trumbore, Ben (1997). "Fast, Minimum Storage Ray-Triangle Intersection". Journal of Graphics Tools. 2: 21–28. doi:10.1080/10867651.1997.10487468.
  2. "Ray-Triangle Intersection". lighthouse3d. Retrieved 2017-09-10.
  3. Ray Intersection of Tessellated Surfaces: Quadrangles versus Triangles, Schlick C., Subrenat G. Graphics Gems 1993
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