(Question) Solid on (3D+) orbit trapping

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Offline FractalDave

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« on: November 13, 2018, 11:46:37 PM »
Just out of interest does anyone know of any maths done to find an analytical method for getting a decent distance estimation for solid based on orbit trapping (at least say for "nearest" and at least for the default trap value i.e. the origin) ?
I have done code previously for solid based on orbit trapping but it was just a brute force method and either a bit inaccurate or a bit slow ! My own formal pure math isn't up to the task :(
If not an analytical one - any other ideas ?
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Offline xenodreambuie

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« Reply #1 on: November 14, 2018, 08:42:27 AM »
Dave, given that orbit traps have arbitrary shapes, which need custom distance functions, I'd be surprised if there can be any analytic solutions for anything much beyond a sphere. So brute force is pretty much it. For ray marching you have bounding volumes to accelerate more complex shapes. (Escape time is brute force but relatively efficient, and inverse methods don't generally use distance functions.) Or am I missing something?

Offline FractalDave

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« Reply #2 on: November 14, 2018, 11:42:24 AM »
By brute-force I meant more than just using the value from a given point, I meant the method I used for my first 3D renders which used the iteration density as a step guide to solid based on iteration count (i.e. the precursor to Buddhi's method which effectively converted it to a true solid based on DE). Unfortunately it doesn't work anywhere near so well when I try it on renders solid based on orbit trapping using the orbit trap colouring density as a loose step guide and AFAIK there isn't a more accurate adaptation of it like the one Buddhi came up with (that actually matches analytical DE very closely and is much faster than the analytical for more complicated formulas and works on some where the analytical method is either extremely difficult or in fact non-existent).

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