Aperiodic Hat Transformations 🎩

Am I doing this right?

In Aperiodic Hat Monotiles the 'Hat' tile is used in a tessellation. Using different ratios for the length of the edges an infinite amount of different shapes are possible for this tessellation (youtu.be/w-ecvtia-5a).

Use the slide for t_morph to 'scroll' through these possibilities. It is a scalar from 0 to 6 (instead of 0 to 1) because there are 6 intervals between the 7 predefined criteria (see lines 56 to 67). The 'hat' is on the 1/3 interval which cannot be expressed with a slider from 0 to 1. With values from 0 to 6 the 'hat' is at value 2.

Using the shoelace approach I solved the problem to keep the area's of the different tile variations the same (lines 86 to 94). However I yet failed to integrate these variations in Aperiodic Hat Monotiles (see Fork: Aperiodic Hat Monotiles) because some transformations are applied to polygons that I do not yet fully understand.

cs.uwaterloo.ca/~csk/hat/
arxiv.org/pdf/2303.10798.pdf

t_morph

2.00

1
2
const t_morph = 2; //min=0 max=6 step=.001
const scale = 20; //--min=0 max=80 step=.5
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