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# Point on a plane

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Hi! I''m trying to project a point (a light actually) onto a plane defined by the 3 verticies of a triangle. Basically I need to move the point along the normal of the plane, some distance t, so that it lies on the plane. I''m reading NeHe''s tutorial on it now (http://nehe.gamedev.net/data/lessons/lesson.asp?lesson=30), and he comes out with this value for t as t= (Xn dot (PointOnRay - Raystart)) / (Xn dot Raydirection) Now.. the RayDirection in this case, is just the normal, and a point on that ray, could be the light it''s self... and the ray start... well... could also be the light... but.. even if I didn''t chose the light, PointOnRay - Raystart will give you the RayDirection.. which is the normal!! Is there something I''m missing here? How can I project my point onto a the nearest point on a plane? -Mr.Oreo

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I''m not thinking clearly today, but I think that is a ray/plane intersection, not the nearest point on the plane. The nearest point on the plane is p-((p-pip).n)*n where p is the point, n is a unit normal for the plane and pip is a point in the plane. (p-pip).n=p.n-pip.n. pip.n is the distance of the plane from the origin in multiples of n and is the same for every point in the plane. p.n is the distance from the origin to a plane containing p which is parallel to the original plane. The distance between the planes is the differance in their distances from the origin. It is a directed distance meaning it can be positive or negative with positive being the same direction as n and negative being in the -n direction. (p-pip).n is the directed distance from the plane containing pip to the parallel plane containing p. ((p-pip).n)*n is a vector from the plane containing pip to the parallel plane containing p. So if you subtract it you have a vector from the parallel plane containing p to the plane containing pip.

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