[//]: <> (hello)

Polyhedra Cut Locus Calculation

Visualize cut loci of the 2-d surfaces of polyhedra

Tested with Python 3.8.10 on Ubuntu (versions 20.04, 22.04, and 24.04) and on Windows 11

[//]: <> (python cut_locus.py -s tetra --legend --font 14 --display-dims 7.5 5.5) [//]: <> (python unfolding.py -s cube --legend --font 11 --display-dims 6.5 5.5) [//]: <> (python unfolding.py -s octa --voronoi --legend --font 11) * Interactive Cut Locus Visualization:

* Path Unfolding Visualization:

* Voronoi Star Unfolding Visualization:

Installation (assuming Python is installed)

• Option 1: Download zip, then extract all

run the following in terminal/command prompt to install Python package:

(replace <name of folder> with path of folder you extracted it to) bash cd <name of folder> pip3 install -e . * Option 2: Clone Repository, then install the python package (assumes Git is installed) bash git clone https://github.com/pranavraj575/polyhedra_cut_locus pip3 install -e polyhedra_cut_locus

Installation Test

Run cut_locus.py from terminal/command prompt in the polyhedracutlocus folder

(move to correct folder with cd <name of folder>)

Example: bash python3 cut_locus.py --shape tetrahedron --center-pt --legend To see the possible arguments, run the following: bash python3 cut_locus.py -h Note: try replacing python3 with python if you get error "Python was not found"

Cut Locus:

Run cut_locus.py from terminal/command prompt in the polyhedracutlocus folder

(move to correct folder with cd <name of folder>)

Example: bash python3 cut_locus.py --shape tetrahedron --center-pt --legend

Path Unfolding:

Run unfolding.py from terminal/command prompt in the polyhedracutlocus folder

Example: bash python3 unfolding.py --shape cube

Voronoi Star Unfolding:

Same as path unfolding, with the additional argument --voronoi-star

Example: bash python3 unfolding.py --shape octahedron --voronoi-star

Implemented shapes:

• Tetrahedron: bash python3 cut_locus.py --shape tetrahedron python3 unfolding.py --shape tetrahedron --voronoi-star [\]: <> (python cutlocus.py -s tetra --source 3 --point -.5 -0.86602540378 --save images/tetrahedron/tetralocusthree.png --display-dims 9 6 --legend --no-show --font 14) [\]: <> (python unfolding.py -s tetra --source 0 --point .5 0.86602540378 --label-unwrapping --save images/tetrahedron/initialvoronoistar.png --display-dims 6.5 5.5 --font 20 --voronoi-star --ignore-points --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/tetrahedron/tetralocusthree.png" width=420 /> <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/tetrahedron/initialvoronoi_star.png" width=420 />

• Cube: bash python3 cut_locus.py --shape cube [\]: <> (python cutlocus.py --shape cube --point .8 .2 --source 2 --legend --display-dims 7 5.5 --save images/cube/democutlocus.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/cube/democut_locus.png" width=690 />

• Octahedron: bash python3 cut_locus.py --shape octahedron [\]: <> (python cutlocus.py -s octa --source 6 --point 0.45 .5 --display-dims 12 6 --font 14 --save images\octahedron\unlabeledlocustau1.png --legend --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/octahedron/unlabeledlocus_tau1.png" width=690 />

• Dodecahedron: bash python3 cut_locus.py --shape dodecahedron --click python3 unfolding.py --shape dodecahedron --click --voronoi-star [\]: <> (python cutlocus.py -s dodeca --source 11 --point 0 0 --display-dims 12 10 --font 17 --save images/dodecahedron/dodecalocuszero.png --no-show) [\]: <> (python unfolding.py -s dodeca --source 0 --point 0 0 --display-dims 11 10 --font 17 --voronoi-star --save images/dodecahedron/dodecastarzero.png --ignore-points --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/dodecahedron/dodecalocuszero.png" width=420 /> <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/dodecahedron/dodecastar_zero.png" width=420 />

• Icosahedron: bash python3 cut_locus.py --shape icosahedron --click python3 unfolding.py --shape icosahedron --click --voronoi-star [\]: <> (python cutlocus.py -s icosa --source 17 --point 0 0 --display-dims 15 10 --font 17 --save images/icosahedron/icosalocuszero.png --no-show) [\]: <> (python unfolding.py -s icosa --source 0 --point 0 0 --display-dims 12 10 --font 17 --voronoi-star --save images/icosahedron/icosastarzero.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/icosahedron/icosalocuszero.png" width=420 /> <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/icosahedron/icosastar_zero.png" width=420 />

• Prism:

  replace <n> with the n-gon you want (3<=n) bash python3 cut_locus.py --shape prism --n <n> [\]: <> (python cutlocus.py --shape prism --n 5 --legend --source 5 --point -.2 .69 --display-dims 9 6 --save images/displayimages/pentagonalprism.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/displayimages/pentagonal_prism.png" width=690 />

• Antiprism:

  replace <n> with the n-gon you want (2<=n) bash python3 cut_locus.py --shape antiprism --n <n> [\]: <> (python cutlocus.py --shape antiprism --n 5 --legend --source 0 --point -1.3 1.5 --display-dims 10 8 --save images/displayimages/pentagonalantiprism.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/displayimages/pentagonal_antiprism.png" width=690 />

• Pyramid:

  replace <n> with the n-gon you want (3<=n<=5) bash python3 cut_locus.py --shape pyramid --n <n> [\]: <> (python cutlocus.py --shape pyramid --n 5 --legend --source 0 --point -.69 .420 --display-dims 12 5 --save images/displayimages/pentagonalpyramid.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/displayimages/pentagonal_pyramid.png" width=690 />

• Elongated Pyramid:

  replace <n> with the n-gon you want (2<=n<=5) bash python3 cut_locus.py --shape longpyramid --n <n> [\]: <> (python cutlocus.py --shape longpyramid --n 5 --legend --source 0 --point .4 -.1 --display-dims 8 5 --save images/displayimages/elongatedpentagonalpyramid.png --no-show)

• Bipyramid:

  replace <n> with the n-gon you want (2<=n<=5) bash python3 cut_locus.py --shape bipyramid --n <n> [\]: <> (python cutlocus.py --shape bipyramid --n 5 --legend --source 0 --point .5 -.8 --display-dims 12 5 --save images/displayimages/pentagonalbipyramid.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/displayimages/pentagonal_bipyramid.png" width=690 />

• Elongated Bipyramid:

  replace <n> with the n-gon you want (3<=n<=5) bash python3 cut_locus.py --shape longbipyramid --n <n> [\]: <> (python cutlocus.py --shape longbipyramid --n 4 --legend --source 0 --point .5 -.8 --display-dims 7 5 --save images/displayimages/elongatedoctahedron.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/displayimages/elongated_octahedron.png" width=690 />

• Torus: bash python3 cut_locus.py --shape torus [\]: <> (python cutlocus.py --shape torus --point .69 .420 --source 00 --display-dims 5.5 5.5 --save images/2torus/sample.png --no-show) <img src="https://github.com/pranavraj575/polyhedracut_locus/blob/main/images/2torus/sample.png" width=690 />

• Mirror (two n-gons glued to each other):

  replace <n> with the n-gon you want (3<=n) bash python3 cut_locus.py --shape mirror --n <n> [\]: <> (python cutlocus.py --shape mirror --legend -n 6 --point .5 .5 --source 0 --display-dims 8 4 --save images/displayimages/hexagonalmirror.png --no-show) <img src="https://github.com/pranavraj575/polyhedracutlocus/blob/main/images/displayimages/hexagonal_mirror.png" width=690 />