I was wondering if it was possible to convert Braycentric coordinates (i.e. u,v) to 3D coordinates (i.e. x,y,z)? If so, how do I do it?

Of course. Though, it requires that you know the two basis vectors which define your u,v subspace. Then, the answer is simply x = b1 * u + b2 * v

Ok, this might sound stupid... What are the basis vectors, and where do I find them?

They are the basis vectors for the subspace in which you are interested in. Its a linear algebra term if you wish to look it up.

The term "barycentric coordinates" is often used in computer graphics on triangles. Given any point on a triangle, in R2 or R3 (in fact in Rn, n >=2), one may find values u,v such that P = V1*u + V2*v, where V1 and V2 are the vectors forming two edges of the triangle sharing a common endpoint, the 0 vector. This can be generalized for situations where one point of the triangle is not the 0 vector, but if the plane of the triangle does not pass through the 0 vector it becomes more complex. It is often conceptually simpler "move" the triangle to this position for finding barycentric coordinates. This way, u,v = 0,0 is mapped directly to one point of the triangle, and IIRC as long as u + v <= 1, P is in the triangle.

It is a convienient way to find points on a 2D plane in 3D space. Think of the u,v coordinates as x,y coordinates. Except, the axes are not (0,1) and (1,0), they are V1 and V2. So, instead of x * (0,1) + y * (1,0), we have u * (a,b) + v * (c,d)

[edited by - MisterAnderson42 on August 27, 2002 1:15:52 AM]

Ok, I think I''ve got it now. Thanks for your help.