In article <4D0C692B.7070400@hawaii.rr.com>, david <gnome@hawaii.rr.com> writes:

Richard wrote:

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The FOTD RSS feed at <http://www.xmission.com/~legalize/fractals/fotd/fotd-rss.xml> is now caught up with the latest images, so you can get nice 1600x1200 3x antialiased renderings of Jim Muth's FOTD series via that feed,

Does "3x antialiased" mean you generate them at 3x the resolution, reduce it to 1600x1200, then antialias it?

More specifically it means 3x oversampling. The images are rendered at 4800x3600 and then filtered down to 1600x1200. This is what most fractal programs do themselves when they render something antialiased, with different amounts of oversampling used by different programs. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

Yes, 4x is slightly better than 3x, but I haven't seen much, if any, aliasing in the 3x. There's a point of diminishing returns with higher multiples. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

In article <4D0EE7AF.2090401@hawaii.rr.com>, david <gnome@hawaii.rr.com> writes:

Richard wrote:

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Yes, 4x is slightly better than 3x, but I haven't seen much, if any, aliasing in the 3x. There's a point of diminishing returns with higher multiples.

I always considered "higher multiples" to be 8x or higher. But that was back in my print days.

The Nyquist-Shannon sampling theorem says that a sampling frequency f cannot possibly represent signals with frequencies greater than 2f. See <http://en.wikipedia.org/wiki/Nyquist_frequency>. Because fractals have "infinite" frequency content, they can never be completely represented at any sampling frequency. The purpose of oversampling and downfiltering a fractal rendering is to bring as much of the signal as possible into the bandwidth represented by the sampling frequency. 2x oversampling is the theoretical rate needed to bring in the entire frequency content that is representable by the output resolution. However, due to the infinite frequency content of fractals, additional oversampling may provide some aesthetic benefit. Some people say that oversampled fractals "look too blurry". This could be due to a poor choice of filter when downsizing the oversampled image to the final resolution. The Mitchell-Netravali filter, see <http://en.wikipedia.org/wiki/Reconstruction_filter>, is one of the few filters in which psychometric experiments were done to determine the most "pleasing" reconstruction in order to avoid aliasing. If you 2x oversample and then use a point filter, you haven't gained anything as the resulting downsampled image with a point filter contains just as much aliasing as the original. (When you sample a fractal at specific points in the complex plane, which is what every fractal rendering program does, you are using a point filter to sample the underlying mathematical construction of a fractal.) The choice of reconstruction filter in the downsampling process has a significant effect on the aesthetics of the downsampled image. Mitchell-Netravali is the best filter I've used; although my RSS feed uses ImageMagick's generic geometry resizing algorithm and its unclear what filter is used by that code, although its clearly an averaging filter and not a point filter. All of the resampling filters have the property that they are low-pass filters -- their whole purpose is to filter off the high frequency components in the oversampled image and replace them with an area based average in the downsampled image. This is, by definition, a process that smooths out the jaggies as the jaggies are high frequency content. I am willing to bet real money that there isn't any distinguishable difference that anyone can see at 8x oversampling or higher. Those contributions are simply gone by the time you downsample that much, particularly at 8 bits per channel. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>