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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > General Discussion > supershape as an isosurface (now dancing)
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Author Topic: supershape as an isosurface (now dancing)  (Read 2750 times)
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DarkBeam
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Fragments of the fractal -like the tip of it
« on: January 27, 2015, 05:38:48 PM »
http://news.povray.org/povray.binaries.images/thread/<405f8589%40news.povray.org>/?ttop=398254&toff=5550

This can be very useful for a DE implementation if correctly implemented smiley
I see lots of redundance so ... simplification should be easy
« Last Edit: January 28, 2015, 06:47:42 PM by DarkBeam » Logged
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cKleinhuis
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« Reply #1 on: January 27, 2015, 05:45:17 PM »
good to know wink certainly worth implementing in gpu as nice isoshape wink
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #2 on: January 27, 2015, 06:51:52 PM »
Super Shape is the most versatile formula imaginable... the image shown is just a sample I think smiley
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cKleinhuis
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« Reply #3 on: January 27, 2015, 08:44:55 PM »
i know the supershape, i once implemented it as transform for a apophysis hack,. and perhaps you ever wondered what the orbit shape was used for these images ? wink

cheesy kiss cheesy

it is very cool to have it as orbit trap, due to the infinite thin/long streaks certain settings of the params produce


some pictures from long time ago


http://www.fractalforums.com/index.php?action=gallery;su=user;cat=4;u=63

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=24
« Last Edit: January 27, 2015, 08:46:38 PM by cKleinhuis » Logged
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youhn
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« Reply #4 on: January 27, 2015, 09:06:16 PM »
Nicely curved  love  but no antialiasing?!  shocked Old looks indeed.
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cKleinhuis
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« Reply #5 on: January 27, 2015, 09:31:57 PM »
yay, curving is great, i have lost the exact method i used to use as orbit distance, and antialiasing was not my concern at that time ... but mutatorkammer is still available in the downloads, a genetical complex formula evolver, sticking together randomly complex formulas with iterative functions as well to produce random escape time fractals wink
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divide and conquer - iterate and rule - chaos is No random!
DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #6 on: January 28, 2015, 12:06:06 AM »
It looks surely nice...
The problem is that MB3D doesn't like a lot strange powers it expects a regular distance field.

Let's hope smiley
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eiffie
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« Reply #7 on: January 28, 2015, 04:25:25 PM »
Well kinda...
https://www.shadertoy.com/view/4llGWM

I'm not sure if you have access to the ray direction in your formulas but I used that to find a 2 point gradient. If you don't then a fudgefactor of around .5 should work on shapes that don't have pointy fan blades. Maybe someone can improve this method??
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #8 on: January 28, 2015, 07:35:24 PM »
 love Eiffie!!! I very very appreciate your help and scripts, but seriously all those passages you do are really necessary? Two SuperShape computations are very computation-heavy! cry
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eiffie
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« Reply #9 on: January 28, 2015, 08:33:26 PM »
Well if you think about it even if we knew how to calc the derivative it would probably be just as expensive as another supershape (or maybe worse). But yes I am looking for better alternatives smiley I am still hoping someone (knighty) will see it and have a breakthru.
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #10 on: January 28, 2015, 11:55:58 PM »
My idea were a rough approx but worked good almost always!

Suppose your implicit is a polynome ...

x^5-x^2-xy+x^2 y^2+x y^3 -3 = 0

Step 1. Find the max exponent. It's 5. P=0 and N=0.
2. Find positive and negative terms.
P= x^2 y^2. (Quadratic)
N = +x^2 +3.
3. Calculate all other terms then add to P if + or to N if -
4. Raise P and N to t=1/(maxexp)
5. DE = pow(P,t)-pow(N,t)

It kinda works good cheesy Try to adapt it...
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eiffie
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« Reply #11 on: January 29, 2015, 05:02:46 PM »
Yes after I thought about it my one-sided gradient wouldn't work at all with folds/rotations so I think an approx is probably the best we can do for now.
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