Hyperbolic tiling iteration problems

Airborne Terror shared this question 2 months ago
Needs Answer

Hi! I'm using Geogebra to make a dynamic hyperbolic tiling in the Poincare Disk such that I can construct any tiling with polygon value "p" and vertex figure "q", from any point inside the Disk and any rotation value from central polygon. so far I have worked around several continuity issues and have managed to construct a stable set of points defining the generator polygon of the tiling (I've loosely followed this tutorial, but no further explanation is provided of how to continue the tiling).

So far I've been using the spreadsheets, but my problems are the following:

1. To continue extending the tiling I need to reflect the set of all points in column "E" in each of the circular arcs of column "F". In order to do that, I made the list "l2={E1:E13}" and set the values in column "L", such that: "L1=Reflect(l2,F1)", "L2=Reflect(l2,F2)"... "...etc". This seems to work fine, but when values of "p" and "q" are changed as to not show the Nth term in column "E", the corresponding Nth list becomes permanently undefined even when the "p" and "q" values are restored and should be able to show it. Is there a way to fix that, or another way to reflect groups of points not involving lists? I tried to replace the lists by using directly "E1:E13" as input, but the same thing keeps happening.

2. Is there a way to ignore/not render points that map to themselves when inverted? there are always two points in column "E" that lie directly on the corresponding arc in column "F", so they map to themselves when reflected, also, I intend to further reflect the points in Column "L", so an algorithm or command that stops points from overlapping would be super useful.

3. This construction requires me to reflect a lot of circular arcs and sometimes they randomly turn into their complementary arcs, is there a way to control this?

4. I'm new to Geogebra and frankly I wouldn't be surprised if there was another, easier way of making this project, I'd love to know if there is. I was also watching this tutorial for a platform called Houdini, and I was wondering if some of the tools used there have proper equivalents in Geogebra.

Thanks in advance!

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