William F Pokorny <ano### [at] anonymousorg> wrote:

> The evaluation point is in the center cubelet of a larger 5x5x5 cube(*)
> of cubelets. The center point of all cubelets is offset by a random-ish
> still within each cubelet as the 'Voronoi' points.
>
> (*) Official POV-Ray does an optimization to calculate only 81 cubelet
> offset vectors & yuqk might later adopt something similar (**). The
> current yuqk crackle is set up for up to 7x7x7 as I wanted to experiment
> with other crackle options at some point.

Right - I forgot about the larger cube dimensions to "catch" the corners.

So, some better thought-out questions are:

How many Voronoi "seeds" are there in the unit cube before you reach the "edge"
and there is a repeat?  Is that / can that be a variable?

What are you doing at the edges/corners to make a space-filling tesselation by
that "unit cube" of Voronoi pattern?  Essentially just a mod (<x, y, z>, N)?



> > Also, have you thought about allowing user-defined distance metrics (Euclidean,
> > Manhattan, Minkowski, etc.) for generating the underlying pattern?
>
> Sure, the first two are already implemented as metrics 2 and 1 (***).
> I'm not completely sure what you mean by minkowski. I'm familiar with
> minkowski sum and difference with respect to shapes. Some options today
> give a similar look, but the devil is in the details.

I guess Minkowski is a generalized form of the first two.
see:
https://www.kdnuggets.com/2023/03/distance-metrics-euclidean-manhattan-minkowski-oh.html

Apparently there's also
Chebyshev
power diagrams - https://en.wikipedia.org/wiki/Power_diagram
weighted Voronoi diagrams -
https://en.wikipedia.org/wiki/Weighted_Voronoi_diagram
https://cs.stackexchange.com/questions/43817/voronoi-diagrams-with-l%E2%88%9E-metric
https://www.researchgate.net/publication/228910426_Visualization_of_Generalized_Voronoi_Diagrams
https://www.researchgate.net/publication/331203691_Computation_of_Compact_Distributions_of_Discrete_Elements

etc

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