I was wondering if anyone knew the math behind the photoshop curves tool (http://www.cambridgeincolour.com/tutorials/photoshop-curves.htm)

basically, i'm just wondering how they calculate the output levels from the input levels - is it just:
http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Higher-order_curves

and if so, any ideas on how to implement the function?

Summary: They're not beizer curves - if I knew what curves they were and how to mathematically express them, that would be amazing (but i don't... yet... T_T )

i'm pretty sure they're not beizer curves (done lots of research since I posted) - remember, beizer curves not only require control points on the line, but there are additional draggable control points that have different properties on the curve based on their distance away from the curve (such as in this picture:
http://en.wikipedia.org/wiki/Image:B%C3%A9zier_curve_in_Adobe_Illustrator_CS2.png )

also, give those four points, beizer curves don't actually go through all the 4 given control points, they only go through 2 as opposed to the curves in photoshop where the curve must go through all of your defined control points


I'm fairly certain (based on dissecting GIMP source code and various other bits of source) that the curves in question are an implementation of "catmull-rom splines"

now according to the processing documentation, this is actually what's called when you run curve() or curveVertex(), but i can't quite get it do work like the photoshop curves do (IE: defining control points using curveVertex() gives a different curve than the same control points in photoshop =/ )

if someone (who is better at java that i am, and that's not saying much because i'm terrible at java) could implement some of the filters at http://www.jhlabs.com/ip/ that would be really cool - i've been trying to tinker with the code there for days to no avail T_T