On Sunday, 07 October 2012, Petr Mikulik wrote:
>Ethan Merritt wrote >
> > There is an option "set pm3d interpolate <xdelta>,<ydelta>" that
> > produces smoother coloring subdividing each quadrangle into smaller
> > quadrangles with individually calculated color values. But these
> > color values are always assign by linear interpolation.
> > For color schemes c1/c2/c3/c4/mean this comes out equivalent to the
> > same overall coloring applied to a finer grid of x,y values. The
> > finer the interpolation, the closer it comes to a true linear color
> > gradient.
> > However, for color schemes using the harmonic or geometric mean,
> > the finer grid still results in a linear color gradient rather than
> > the requested geometric or harmonic color variation. Shouldn't the
> > interpolation in these cases be some non-linear function?
> > What function would that be?
> Coordinates x, y can be interpolated linearly, but the colour coords can
> follow arithmentic, geometric or harmonic mean.
Sure, but what are the corresponding interpolation functions?
If the c1/c2/c3/c4 quadrangle is to be colored using a harmonic mean,
and interpolation 3,3 splits adds four new vertices in the interior,
what is the proper interpolated color at those new vertices?
Clement Law <themanifold@...> wrote>
> I've written up another pm3d corners2color function. It works just as
> the others, i.e.,
> set pm3d corners2color rms
> rms4 takes the root mean square of the four corners
Do you see what I'm asking about how to handle interpolation
for these non-linear coloring schemes?