Ray-tracing quaternions/hypercomplex fractals

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MakinMagic 101 Aug 19, 2009 at 15:44

Has anyone worked on a method for efficiently ray-stepping through the “inside” of 3D+ non-affine fractals ?
I’m asking as I am working on code to ray-trace fractals that will include transparency/diffraction.
So far the only relevant text I’ve found is the brief outline on Wikipedia regarding Distance Estimation for the “inside” but the algorithm requires too many iterations and is not generic enough for the purposes of rendering general 4D number systems.
I’d appreciate any thoughts on the subject :)

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SyntaxError 101 Aug 19, 2009 at 17:55

I don’t really know much about ray tracing but I think Mojoworld uses it. There is an algorithm in “Texture & Modeling A procedural Approach, third edition” but I’m not sure if it’s even close to what you need. I haven’t looked at it in detail because I’m not doing ray tracing. I bought Mojoworld just to try it out but the frame rate is pretty low. It’s engine would not be suitable for games, but it’s still a cool program.

In any case your problem sounds like a Kenton Musgrave sort of thing. I think he either started Pandromeda (they sell Mojoworld) or at least he works there. He’s also a pretty famous author and fractal expert. He sent me email personally when I some issue installing the program. We even had a short email exchange. He sounded like a supper nice guy. You might want to look into his work or contact him.

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MakinMagic 101 Aug 19, 2009 at 21:28

Thanks very much, I’ll give contacting him a try…

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flux00 101 Aug 20, 2009 at 01:41

Why can’t you simply trace a ray toward the fractal from the other side with exactly the opposite direction?

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MakinMagic 101 Aug 20, 2009 at 15:20

@flux00

Why can’t you simply trace a ray toward the fractal from the other side with exactly the opposite direction?

Well that would work if all fractals were 100% convex but if they were then they probably wouldn’t be fractals :)

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flux00 101 Aug 27, 2009 at 03:37

What?

Once you already have the intersection algorithm it’d be easy.

You can also do something similar with refraction.

Untitled-4.jpg

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Reedbeta 167 Aug 27, 2009 at 03:53

I think he’s talking about cases where a ray could have more than two intersections with the fractal; it could go in, go out, then go in again somewhere else and go out again. In your diagram, this could happen if the ray was vertical.

In that case if there’s no distance function that works well inside the fractal, it seems like it could be hard to find all the intersections. At least that’s what I think the OP is getting at.

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rouncer 103 Aug 27, 2009 at 10:29

The only fractals i can think of form octrees, imagine a 3dtilemapped octree that always invites new detail.