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Knighty, looks to me like your rays are missing the back part of the object as they pass through the holes. Try putting in a condition that your distance estimate can never increase. In other words, keep track of the DE as you step on the ray and if the DE is larger than a previous value on that ray, take the smaller value..

Just got the animation feature working with the extended parameters and made a little sierpinski morph.
More randomly choosen parameters, but some spots are ok i think:

<a href="http://vimeo.com/moogaloop.swf?clip_id=11816563&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=11816563&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>

Wow, this sequence is simply stunning!
Just love those "living" forms, especially the part from 01:02 to 01:30...

Just a fake AO based on z-buffer and phong shading with up to 4 lights in infinity positions, so i only need 2 angles for them.
Have some improvements in mind to get a better AO that takes care of the background and object colors.


Is also my favorite part  

Knighty, I think the reason your icosa looks the way it does, is because you apply your pre-rotations outside the DE-loop (the left image). If you put the rotations inside the loop (the right image), it seems quite solid.



Of course this slows down the rendering since you have to apply the reflections five times each iteration.

I use the x,y,z (abs) reflection to speed up the calculation a bit:

while (n < maxIterations) {
    p = abs(p); // saves us three repetitions
    if (dot(p, n1)>0) { p *= n1Mat; } // rep 1
    if (dot(p, n2)>0) { p *= n2Mat; }
    if (dot(p, n3)>0) { p *= n3Mat; }
    if (dot(p, n1)>0) { p *= n1Mat; } // rep 2
    if (dot(p, n2)>0) { p *= n2Mat; }
    if (dot(p, n3)>0) { p *= n3Mat; }
    p = p*scale - offset*(scale-1.0);
       
    if (dot(p, p) > bailoutSquared) break;
    n++;
}

Does anyone know of a faster way to reduce the number of reflections? Perhaps it is possible to transform to a new coordinate system, where the normals are perpendicular and axis-oriented, and use the fast 'abs' operator, before transforming back?

And, btw, thanks for a very interesting thread. These systems are truly fascinating.

Hi, just wanted to share some images created with the hollow (pre-rotated) Icosahedron variant.








(All rendered on a GPU using Subblue's Pixel Bender raytracer)

Best, Mikael.

Here is what I find:
The tetra, the octa and the cube need 3 folds.
The dodeca and the icosa need 5 folds.
So the sequence is : fold around the three symmetry planes n times, scale from fixed point, fold n times, scale...etc.

BTW, the treshold scale value above which the polyhedron is not smooth anymore is :
1.5 for the tetra, dodeca and icosa
2.0 for the cube
1+phi/2 (about 1.8..) for the dodeca.

Can anyone assist with the icos and dodec folding code?  I cannot follow the snippets so far.
I am using Knighty's method for folding like this for the full octahedral.  What should the folding code look like in this sort of format for icosa and dodeca?


Here is another sample movie.  Must be seen in full HD for all the finer details.

<a href="http://www.youtube.com/v/XxfoPq_eKAE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/XxfoPq_eKAE&rel=1&fs=1&hd=1</a>

The pre-rotate technique is great too.  Opens up another layer of parameter space to search.

Jason.