On Tuesday, 20 September 2016 at 12:35:18 UTC, Basile B. wrote:
I've recently started an easing/interpolation family of function in my D user library. It's based on something I know well since I've already used them in 2012 in a VST plugin called GrainPlot (RIP).


However for one of the function, I can't manage to get the inverse.
[...]
The problem is here:
https://github.com/BBasile/iz/blob/master/import/iz/math.d#L849
- f(x,c) = 1.0 - pow(1.0 - pow(x, 2.0/c), c * 0.5);
- c(f0.5)) = ?

Which means that I ask you if you can isolate c for

y = 1.0 - pow(1.0 - pow(0.5, 2.0/c), c * 0.5);

y is always f(0.5,c)

If you don't understand, these function have a control point, for "parabol" and "pow" it's easy to get the c Coefficient that manages the slope. But for the ellipse (aka the super ellipse) it's a math nightmare !!!!)

For example is use the three functions in the same order (parabol, pow, ellipse):

http://sendvid.com/ygti5jmr

for the ellipse you can see that the mouse position is not in sync with the control point at the middle...it's the problem.

I need to isolate c when "y = 1.0 - pow(1.0 - pow(0.5, 2.0/c), c * 0.5)".
I know it's hard...otherwise I wouldn't ask ;]


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