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

This question is old but since there is such a much more convenient solution I figured it might help someone.

Plane and line intersections are quite elegant when expressed in homogeneous coordinates but lets assume you just want the solution:

There is a vector 4x1 p which describes the plane such that p^T*x =0 for any homogeneous point on the plane. Next compute the plucker coordinates for the line L=ab^T - ba^T where a = {point_1; 1}, b={point_2;1}, both 4x1 on the line

compute: x=L*p = {x0,x1,x2,x3}

x_intersect=({x0,x1,x2}/x3) where if x3 is zero there is no intersection in the euclidean sense.