3D Line-Plane Intersection

Question

If given a line (represented by either a vector or two points on the line) how do I find the point at which the line intersects a plane? I\'ve found loads of resources on th

Answer 1

If you have two points p and q that define a line, and a plane in the general cartesian form ax+by+cz+d = 0, you can use the parametric method.

If you needed this for coding purposes, here's a javascript snippet:

/**
* findLinePlaneIntersectionCoords (to avoid requiring unnecessary instantiation)
* Given points p with px py pz and q that define a line, and the plane
* of formula ax+by+cz+d = 0, returns the intersection point or null if none.
*/
function findLinePlaneIntersectionCoords(px, py, pz, qx, qy, qz, a, b, c, d) {
    var tDenom = a*(qx-px) + b*(qy-py) + c*(qz-pz);
    if (tDenom == 0) return null;

    var t = - ( a*px + b*py + c*pz + d ) / tDenom;

    return {
        x: (px+t*(qx-px)),
        y: (py+t*(qy-py)),
        z: (pz+t*(qz-pz))
    };
}

// Example (plane at y = 10  and perpendicular line from the origin)
console.log(JSON.stringify(findLinePlaneIntersectionCoords(0,0,0,0,1,0,0,1,0,-10)));

// Example (no intersection, plane and line are parallel)
console.log(JSON.stringify(findLinePlaneIntersectionCoords(0,0,0,0,0,1,0,1,0,-10)));