Mapping images into fractal renders

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Offline FractalDave

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« on: November 23, 2018, 04:50:06 PM »
Just saw an old topic asking about software for this but no mention in the thread anywhere about methods, I was going to post the following there but the thread was old and I guess it's better here anyway.....

Just to add a mention of method to the madness here, I know only of 5 methods (for 2D anyway):

1. The original atan of (escape) angle and the potential ("outside" only)
2. The potential and true (or close) field lines ("outside" only) e.g. my avatar thumbnail to the left uses this in polar coords.....
3. DE and equivalent to field lines for that ("outside" only) - or mix with final atan ?
4. Any type of orbit trap with 2D+ trap value - just map from image using 2 (of the) trapped floats (anywhere really)
5. Specifically from 4 A double orbit trap using two lines or two curves etc. using the trap distance from each (preferably the two traps being perpendicular at least in some areas) (anywhere really)

Any more ?
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Offline pauldelbrot

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« Reply #1 on: November 23, 2018, 08:10:53 PM »
Interior: use real and imag part of derivative around one period. That's how this was rendered:

 :wow:

Offline FractalDave

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« Reply #2 on: November 24, 2018, 02:13:17 AM »
Ah, yeah, in fact you could even trap the derivative too ;)

Edit: Or use the derivative's potential/angle/field lines or (in some cases?) even calculate the 2nd derivative and thus use DE values for the first ;)

Interior: use real and imag part of derivative around one period. That's how this was rendered:

 <snip>

Offline xenodreambuie

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« Reply #3 on: November 24, 2018, 09:11:51 PM »
Taking the potential, DE or other measure as a heightfield, calculate the gradient and project into an environment map.

Offline FractalDave

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« Reply #4 on: November 25, 2018, 03:20:55 AM »
Taking the potential, DE or other measure as a heightfield, calculate the gradient and project into an environment map.

Thanks Grant, you expressed what I was trying to say in the simplest and most generic way possible :)
Of course in specific cases there's a better option than the brute-force gradient as a perpendicular - at least in computational terms.

Offline xenodreambuie

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« Reply #5 on: November 25, 2018, 08:14:59 AM »
You can optimize the gradient calculation for specific measures analytically or just take forward differences. As long as you end up with a surface normal, you have flexibility in choice of projection and map type.