Line-Plane Intersection STEP 1 : KNOWNS The equation of a line is: P = P0 + t(P1 – P0) - P  is any arbitrary point on the line.  In this case, P is the point of intersection of the ray and the plane - P0 is the starting point of the line - P1 is the end point of our line segment - t is the parameter.  Values between 0 and 1 represent points on our line. The equation of a plane is: N dot (P – P2) = 0  - N is the normal of the plane - P and P2 are known points on the plane.  In this case, P will represent the point of intersection. If our plane was represented by a triangle, P2 could be one of the vertices. STEP 2 : PLUG AND CHUG Plug the equation of the ray into our intersection pt of the equation of the plane. N dot ( (P0 + tV) – P2) = 0   Solve for t: (N dot (P0 + tV)) – (N dot P2) = 0 (N dot (P0 + tV)) = (N dot P2) (N dot P0) + (N dot tV) = (N dot P2) N dot tV = (N dot P2) - (N dot p0) t = N dot (p2 – p0)      N dot V   Note: If N dot V = 0, then the line segment is perpendicular to the Normal of the plane, meaning the plane and line-segment are parallel, no intersection. STEP 3 : FINISHING UP Now that you have t, plug it into our equation for a line: P = P0 + t(P1 – P0)   And you’ll get the coordinates of the intersection point Notes on T: If: t > 0 and t < 1  :           The intersection occurs between the two end points t = 0                 :           The intersection falls on the first end point t = 1                 :           Intersection falls on the second end point t > 1                 :           Intersection occurs beyond second end Point t < 0                 :           Intersection happens before 1st end point.