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brsr committed May 31, 2019
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Expand Up @@ -8,19 +8,15 @@ Manipulation of polyhedra and tilings using Python. This package is designed to
pip3 install git+git://github.com/brsr/antitile.git

## Usage
The package includes a number of scripts. These can be piped together with programs from Antiprism:
The package includes a number of scripts.
* `gcopoly.py`: The Goldberg-Coxeter subdivision operation of tilings
* `balloon.py`: Balloon tiling of the sphere
* `cellular.py`: Colors polyhedra using cellular automata
* `nslerp.py`: Naive slerp surfaces
* `gcostats.py`: Statistics of the polyhedra/tiling, focused on the use of GCO to model the sphere (see also `off_report` in Antiprism)
* `view_off.py`: A viewer for OFF files using matplotlib, allowing for export to SVG (see also `antiview` in Antiprism)

These are free-standing:
* `breakdown.py`: Visualize breakdown structures
* `factor.py`: Factors Gaussian, Eisenstein, Steineisen (Eisenstein expressed with the 6th root of unity instead of 3rd), and regular integers.

OFF files for the regular icosahedron, octahedron, tetrahedron, cube, and 3- and 4-edged dihedra are included in the `data` folder in the source.
Some Jupyter notebooks exploring various aspects of these programs are included in the `misc` folder in the source, as well as some OFF files for simple polyhedra including the 3- and 4-dihedra.

## Examples
Statistics of a geodesic polyhedron (created using what geodesic dome people call Method 1):
Expand All @@ -34,13 +30,13 @@ Visualize a Goldberg polyhedron, with color:
Create a quadrilateral-faced similar grid subdivision polyhedron, put it into canonical form (so the faces are all flat), and color it using Conway's Game of Life with random initial condition:

gcopoly.py -a 5 -b 3 cube.off | canonical | off_color test.off -f n | cellular.py -v -b=3 -s=2,3
view_off.py cellular100.off
view_off.py cellular100.off
# or whatever the last file is if it reaches steady state early

`gcopoly.py` can subdivide non-orientable surfaces too, at least for Class I and II subdivisions. Here, the base is a Möbius strip-like surface with 12 faces:

unitile2d 2 -s m -w 4 -l 1 | gcopoly.py -a 2 -b 2 -n | view_off.py
unitile2d 2 -s m -w 4 -l 1 | gcopoly.py -a 2 -b 2 -n | view_off.py

A quadrilateral balloon polyhedra, which happens to resemble a peeled coconut:

balloon.py 8 -pql | view_off.py
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