How to recreate the math behind photoshop curves

Question

Basically, what I want to do is understand how to calculate the values along a \'curve\' as represented here in the photoshop curves box:

Answer 1

Photoshop uses an interpolating cubic spline for the curve, as explored on a separate Math StackExchange thread.

Answer 2

I'm not familiar with C-R, but if it's like beziers, than the T parameter varies from 0 at one endpoint of a curve section to one at the other end point. It's how you "step along" the curve. So you can't just plug an x value you in. You can either sample a long at some arbitrary interval or you can use some sort of goal seeking algorithm to approach a given x value to whatever amount of precision you deem necessary.

Answer 3

A Catmull-Rom Spline is used because it's a kind of spline that represents a curve in which you can add control points and refine the curve itself (that is what you do on Photoshop when you click to add a new point), with the particularity to have the curve pass by every control point you specify.

In any case you just need a function that taken a value (float in 0..1 or int in 0..255 or whatever color space you have) will produce another one.

float fun(float x) {
  y = /* something */
  return y;
}

This can be done with whatever kind of function of course. The most basic one is the default one that is an identity function

float fun(float x) {
  y = x;
  return y;
}

Any other function can be calculated with curves and it will be ok but more complex to develop, I'd suggest you to start from simple examples like a Bezier curve. In any case the t parameter is used because these are parametric curves, you need to understand some of the mathematical background of curves before digging into development, take a look here.

Answer 4

Here's a link to a vbscript that appears to implement the cubic-spline curves photoshop uses.

http://www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=68577&lngWId=-1

Answer 5

This code appears to match Photoshop's curves exactly (not my code): http://www.developpez.net/forums/d331608-3/autres-langages/algorithmes/contribuez/image-interpolation-spline-cubique/#post3513925