supershape as an isosurface (now dancing)

[DarkBeam]

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
I see lots of redundance so ... simplification should be easy

[cKleinhuis]

good to know certainly worth implementing in gpu as nice isoshape

[DarkBeam]

Super Shape is the most versatile formula imaginable... the image shown is just a sample I think

[cKleinhuis]

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 ?



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

[youhn]

Nicely curved    but no antialiasing?!  Old looks indeed.

[cKleinhuis]

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

[DarkBeam]

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

[eiffie]

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??

[DarkBeam]

  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!

[eiffie]

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 I am still hoping someone (knighty) will see it and have a breakthru.

[DarkBeam]

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 Try to adapt it...

[eiffie]

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.