At first i was going to snub the linear idea, but now that i think about it, that's how a "color ramp" would work anyway, isn't it? Maybe i'm making the whole thing much too over complicated.
Like let's say i have this (letters represent colors in a gradient):
A--------------B---------------------------------C ^
At the specified point, the color would be about 25% B and 75% C. That's very easy to figure out.
If i missed something, please let me know. It's not all a waste, i did go explore Lagrange interpolation for an hour or two and almost had a new class debugged for it. I even relearned Sigma and Pi Notation ;-)