Non-linear interpolation

[LeaVerou]

Right now we only support linear interpolation.

We should also support:

• Custom cubic bezier
• Possibly keywords
• Entirely custom functions

[svgeesus]

Interpolation with curves can produce out of gamut values due to curve overshoot. It is desirable to minimize this, and come curve interpolation methods have no overshoot.

This overview of interpolation mentions cosine interpolation, which is very straightforward code-wise and avoids the obvious discontinuities produced by linear interpolation, while having no overshoot:

[svgeesus]

compare

double LinearInterpolate(
   double y1,double y2,
   double mu)
{
   return(y1*(1-mu)+y2*mu);
}

with

double CosineInterpolate(
   double y1,double y2,
   double mu)
{
   double mu2;

   mu2 = (1-cos(mu*PI))/2;
   return(y1*(1-mu2)+y2*mu2);
}

[LeaVerou]

Closing this since we already have non-linear-interpolation, and opened #410 to track shortcuts