Pixel Bender: Cairo Tiling

I realized I had plenty of interesting stuff in my archives, so my next postings will be some pixel bender-filters I’ve done – but no 3D yet. I might have posted already some screenshots of these on my Flickr-account.
Cairo Tiling is made out of pentagonal tiles. Unlike in many other surface filling tilings, here the polygons are not regular.


Click on above image to go to the demo. Set the pattern size to zero to see the source image. Settings the parameter ’tiling truncation’ to -0.13 gives you a Snub Square Tiling.

But how to do that with code? On the first sight one might thing a lot of mathematics are required to handle all the lines in different angles and everything.
But no, if you place a regular orthogonal grid upon the image, things start to clear out:

Now there is a regular pattern inside every rectangular cell. Every other one is mirrored, handling the tilted coordinates is not that hard.

View the sources here.
Download sources.
Pixel Bender -source code.
Pixel Bender -filter.
And quite interesting things start showing up, if the same image is filtered twice: