3D line plane intersection, with simple plane

Question

i have two points in 3D space which have X-coordinates with different signum. so one of them lies definitely on one side of the X-plane and one on the other.

now i w

Answer 1

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

The general case is very nearly exactly as fast in practice if correctly implemented.

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^Tx =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=Lp = {x0,x1,x2,x3} x_intersect=({x0,x1,x2}/x3)

For higher performance use of expressions templates will allow the compiler to collapse the solution to the minimal case.