Fractalforums

Fractal Software => Programming => Topic started by: unassigned on August 24, 2020, 11:36:17 PM

Title: Keyframe interpolation, series approximation and periods.
Post by: unassigned on August 24, 2020, 11:36:17 PM
Hi everyone,

I've been working on my own mandelbrot renderer and I have a few questions around how these are done:

1. How does the current method for keyframe interpolation work? I understand that keyfames can be generated at different zoom levels (such halving each keyfame), but from what I understand if these were interpolated, there would be a loss of quality in between each keyframe.

2. For series approximation, what methods of determining probe points work best? I currently am only using the 4 corners as probes but this overskips quite often. I've read that using some NR iterations to place a probe point near a minibrot may work well but has this been tested (what does KF use)?

3. For the algorithm I use for reference and perturbation calculations, sometimes the center point is very close to zero and periodically does this. I think this is the minibrot period. Is the reference orbit the same after each of these near-zero approaches, and could this be used to speed up reference calculations?

Also, is there any program currently that can color and assemble a zoom video using the OpenEXR output data file format?
Title: Re: Keyframe interpolation, series approximation and periods.
Post by: claude on November 09, 2020, 06:27:53 PM
if these were interpolated, there would be a loss of quality in between each keyframe.
yes, that is why I switched to exponential map: https://mathr.co.uk/blog/2020-06-18_optimizing_zoom_animations_again.html much more efficient, so the same effort gives better quality

Quote
using the 4 corners as probes but this overskips quite often.
KF uses the 4 corners plus the 4 midpoints of the view sides.  It compares series with regular (perturbed) iterations iirc, and has two thresholds (the stricter one is enabled with "approx low tolerance" checkbox)

Quote
I've read that using some NR iterations to place a probe point near a minibrot may work well
I think this might be what knighty's SuperMB does, not sure

Quote
Is the reference orbit the same after each of these near-zero approaches, and could this be used to speed up reference calculations?
there is a unique periodic point (nucleus) at the center of each minibrot cardioid (and disc, but maybe that's not so useful?) that returns exactly to 0 and repeats with a set period, which is a good reference to pick - you still need to update the series approximation coefficients (but if you use a series in 2 variables you only need to do it for 1 period - this is knighty's NanoMB technique).  kf doesn't use periodicity of references outside of nanomb code (for power 2 mandelbrot only).  mandelbrot-perturbator uses periodicity of references and properties of perturbation to not need to restart iterating pixels when they are glitched, too.

Quote
Also, is there any program currently that can color and assemble a zoom video using the OpenEXR output data file format?
https://mathr.co.uk/zoomasm can, some months after you asked (it uses EXR input in exponential map layout (e.g. output from KF), does not (yet) output EXR video frames but that could be interesting for HDR).