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.


A function that's fully implemented:
https://github.com/BBasile/iz/blob/master/import/iz/math.d#L598
- f(x,c) = x*x*x - x*x*c + x*c;
- c(f(0.5)) = 4 * (y - 0.125));

Another:
https://github.com/BBasile/iz/blob/master/import/iz/math.d#L749
- f(x,c) = pow(x, c);
- c(f(0.5)) = log(y) / log(0.5));

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)

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