Non-Linear color interpolation?

Question

If I have a straight line that mesures from 0 to 1, then I have colorA(255,0,0) at 0 on the line, then at 0.3 I have colorB(20,160,0) then at 1 on the line I have colorC(0,0

Answer 1

In the abstract, you're asking for the value of f(0.7) given that f(0.0) = (255, 0, 0), f(0.3) = (20, 160, 0), and f(1.0) = (0, 0, 0). As stated, this isn't well-defined as f could be any of an infinite number of functions.

Some possible choices for f are:

1. A series of line segments in RGB space
2. A series of line segments after mapping to HSV or HSL space
3. A cubic spline in RGB space.
4. A cubic spline in HSV/L space.

But the particular choice of how f should be defined should depend on what you're doing, or how the color stops are defined for your application.