3D Line Segment and Plane Intersection

Question

I'm trying to implement a line segment and plane intersection test that will return true or false depending on whether or not it intersects the plane. It also will return the contact point on the plane where the line intersects, if the line does not intersect, the function should still return the intersection point had the line segmenent had been a ray. I used the information and code from Christer Ericson's Real-time Collision Detection but I don't think im implementing it correctly.

The plane im using is derived from the normal and vertice of a triangle. Finding the location of intersection on the plane is what i want, regardless of whether or not it is located on the triangle i used to derive the plane.

The parameters of the function are as follows:

contact = the contact point on the plane, this is what i want calculated
ray = B - A, simply the line from A to B
rayOrigin = A, the origin of the line segement
normal = normal of the plane (normal of a triangle)
coord = a point on the plane (vertice of a triangle)

Here's the code im using:

bool linePlaneIntersection(Vector& contact, Vector ray, Vector rayOrigin, Vector normal, Vector coord) {

    // calculate plane
    float d = Dot(normal, coord);

    if (Dot(normal, ray)) {
        return false; // avoid divide by zero
    }

    // Compute the t value for the directed line ray intersecting the plane
    float t = (d - Dot(normal, rayOrigin)) / Dot(normal, ray);

    // scale the ray by t
    Vector newRay = ray * t;

    // calc contact point
    contact = rayOrigin + newRay;

    if (t >= 0.0f && t <= 1.0f) {
        return true; // line intersects plane
    }
    return false; // line does not
}

In my tests, it never returns true... any ideas?

Answer 1

I could be wrong about this, but there are a few spots in the code that seem very suspicious. To begin, consider this line:

// calculate plane
float d = Dot(normal, coord);

Here, your value d corresponds to the dot product between the plane normal (a vector) and a point in space (a point on the plane). This seems wrong. In particular, if you have any plane passing through the origin and use the origin as the coordinate point, you will end up computing

d = Dot(normal, (0, 0, 0)) = 0

And immediately returning false. I'm not sure what you intended to do here, but I'm pretty sure that this isn't what you meant.

Another spot in the code that seems suspicious is this line:

// Compute the t value for the directed line ray intersecting the plane
float t = (d - Dot(normal, rayOrigin)) / Dot(normal, ray);

Note that you're computing the dot product between the plane's normal vector (a vector) and the ray's origin point (a point in space). This seems weird because it means that depending on where the ray originates in space, the scaling factor you use for the ray changes. I would suggest looking at this code one more time to see if this is really what you meant.

Hope this helps!