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SomeCodeGuy

Simple question on Plane equation

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Hi there, We all know that the equation to a plane is: Ax + By + Cz + D = 0 and we also know that if I have the Normal of the plane, say, N = [Nx Ny Nz] then I can just make a plane equation like this: (Nx)x + (Ny)y + (Nz)z + D = 0 Ok... and now my question: In the above equation, if N is a UNIT normal, meaning |N| = 1, what is the value of D ?? I have a feeling that D, in this case, is 1. Am I correct?? Thanks

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D=-((Nx)x + (Ny)y + (Nz)z) where (x,y,z) is any point on the plane I believe mag*Nx is the x coordinate of the closest point on the plane and that would make D=-mag*(Nx^2+Ny^2+Nz^2) and (Nx^2+Ny^2+Nz^2) = 1 so perhaps D=-mag or maybe the distance of the plane from the origin. Math isn''t my strong suite though.

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I found out some more about the value D at http://nate.scuzzy.net/normals/normals.html, where the author says:

"The D value of the plane equation represents the distance of the plane to the origin only when the normal is unit length."

Hmm... the distance of the plane to the origin... now what in the world is that mean?? A plane is composed of an infinite number of points, and thus can have an infinite number of distances to the origin... Is he talking the SHORTEST distance to the origin??

*sigh*

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yes, D is the shortest distance to the origin. It is the number that allows you to uniquily define a plane.

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