Distance Estimators Comparison by MakinMagic

Distance Estimators Comparison by MakinMagic

Created using Ultra Fractal.

These images give a direct comparison between the analytical distance estimator and the "delta" distance estimator as applied to the z^2+c quaternionic Mandelbrot.

All 4 renders where done @3840*2880 pixels.
The analytical DE renders took 9mins 17 secs and 12mins 5secs.
The delta DE renders took 13mins 36secs and 19mins 52secs.

As expected the delta method is somewhat less than twice as slow as the analytical one (the difference in speed being primarily due to the delta method requiring 2 iteration loops per ray-step rather than just one).

beason Featured By Owner Nov 4, 2009

Why are the shadows more pronounced in the Delta DE images? Are they rendered with different shading or do they just have more detail?

MakinMagic Featured By Owner Nov 5, 2009 Hobbyist Digital Artist

I did the coordinate calculation for the points for calculating the normals assuming that the DE values when close to solid are 100% accurate i.e. assuming perfect linearity of the distance estimate. This is not completely correct in either the delta DE case or the analytical DE case, though it's more accurate for analytical DE and the difference in the deviation from linearity results in the different shading.
There would be less difference if a "full" or partial ray-trace was done for the adjacent points to get the normals but that takes a lot longer in UF due to not being able to either pass coordinate data from one screen pixel to another and not being able to post-process from a z-buffer.
I realise there is a way around that in UF - specifically calculations could be done to a full-screen buffer in the global section *but* then you can't render large print-size images such as say 8000*6000 (the limit being more like 4000*3000).