I'm a Computing Science student from the Netherlands and I'm currently writing my master's thesis about texture synthesis for data visualization. I've created a model with 3 main parameters (u, v, and c) to generate textures. The position of these textures in a perceptually uniform texture space is given by <x,y,z> coordinates, which are derived from u, v, and c. In essence, x, y, and z are functions of u, v, and c.
I would also like to be able to determine what u, v and c values correspond to a certain <x,y,z> point by making u, v and c functions of x, y, and z. I started by entering my UVC-to-XYZ functions into Mathematica (a system of 3 equations; one for x, y, and z, respectively) and trying to solve for u, v, and c (ending up with XYZ-To-UVC functions), but Mathematica returned the error that "The equations appear to involve the variables to be solved for in an essentially non-algebraic way.".
The Mathematica notebook can be found at http://danny.inforumweb.nl/XYZToUVC.nb. If someone would be willing to tell me what I'm doing wrong and how to perform the required operations, I would greatly appreciate it. Thanks in advance.