Hi Gath,

Stochastic sampling (1) is a method for trading aliasing for noise. Result are neither alias free nor noise free. But it allows using Ray Tracing and related techniques, and that is great for photorealistic rendering of 3D stuff. This the kinds of problems Pixar works on.

OTOH, I focus in 2D vector graphics, and not in 3D rendering. And yes, common implementations of OpenGL and libraries such as Cairo and AGG don't do prefiltering (called 'Analytical Algorithms' by Cook).

I hope this helps.

Cheers,
Juan Vuletich

(1) http://www.cs.virginia.edu/~gfx/Courses/2003/ImageSynthesis/papers/Sampling/Stochastic%20Sampling%20in%20Computer%20Graphics.pdf

Quoting Gath-Gealaich <gath.na.geala...@gmail.com>:

On Tue, 03 Dec 2013 23:24:12 -0300
"J. Vuletich (mail lists)" <juanli...@jvuletich.org> wrote:

Hi Folks,

The first defensive disclosure about Morphic 3 has been accepted and
published at
http://www.defensivepublications.org/publications/prefiltering-antialiasing-for-general-vector-graphics
and http://ip.com/IPCOM/000232657 ..

Morphic 3 is described at
http://www.jvuletich.org/Morphic3/Morphic3-201006.html

On http://www.jvuletich.org/Morphic3/Morphic3-201006.html, you claim:

Anti-aliasing is usually considered a technique to avoid "stairway"
artifacts on rendered images. This is a simplistic view on the
problem. Aliasing is a consequence of sampling continuous functions
(images, photos, sound, etc). Makers of digital cameras and audio
software know and use the theory behind it. You can read more at
http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem.

Researches know all this. The best text books say it. However,
existing graphics software completely ignore the theory.

... This allows for mathematically proved alias free rendering. As no
existing application does this ...

I'm sort of puzzled by this. I've always thought that this was the
whole idea behind the stochastic sampling thingy that the ILM/Pixar
people patented (http://www.google.com/patents/US4897806) in the 1980's
to achieve mathematically proven alias-free rendering (as you said) of
arbitrarily shaded arbitrary geometry (even shaded with non-analytical
functions). Of course, it trades aliasing for noise, but I believe
that you can have the noise arbitrarily low (and for animations, it may
not matter all that much anyway since one can expect some grain or
noisiness on live footage so completely noise-free sampling may even
look unnatural). They certainly didn't ignore the problem; they had
been studying numerous analytical and non-analytical solutions for a
better part of the 1980s and then finally striked gold with stochastic
sampling and PRMan.

-- Gath
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Cheers,
Juan Vuletich

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