squircle 0.2.2

squircle.py is a Python utility for stretching circles into squares and squishing squares into circles. It requires Python 3.6 or later.

Installation

pip install squircle

Usage:

import numpy as np
from PIL import Image

from squircle import to_circle, to_square

square = np.asarray(Image.open('some-square-image.jpg'))
circle = to_circle(square)
and_back_to_square = to_square(circle)

there's 3 stretching methods you can choose from

>>> from squircle import methods
>>> list(methods.keys())
['fgs', 'stretch', 'elliptical']
>>> circle = to_circle(square, method='elliptical')

Stretching methods

Fernández-Guasti squircle (fgs)

The Fernández-Guasti squircle is used by default.

https://squircular.blogspot.com/2015/09/fernandez-guastis-squircle.html

http://mathworld.wolfram.com/Squircle.html

Simple Stretching (stretch)

This method "just linearly stretches each point radially so that the rim of the circle matches the rim of the square".

https://squircular.blogspot.com/2015/09/elliptical-arc-mapping.html

Elliptical grid mapping (elliptical)

"The way I went about this was to think of a line of constant x (as well as a line of constant y) getting mapped to an ellipse in the circle"

https://mathproofs.blogspot.com/2005/07/mapping-square-to-circle.html

https://squircular.blogspot.com/2015/09/mapping-circle-to-square.html

Schwarz-Christoffel conformal mapping

raise NotImplementedError. The math is difficult.

https://squircular.blogspot.com/2015/09/schwarz-christoffel-mapping.html

http://jcgt.org/published/0005/02/01/

Development

After pip install tox you can run squircle's (limited) test set with

tox

On Ubuntu, you also need the following dependencies for numpy and matplotlib

sudo apt install python3-dev libjpeg-dev zlib1g-dev libfreetype6-dev

You can visually inspect the transformations by uncommenting the matplotlib code in test_squircle.py and then invoking the tests directly with pytest instead of tox

pytest

but you'll need to install the dependencies of the tests manually, which you can do with pip install pytest numpy matplotlib pillow.

TODOs

If you would like to help with this project, the open issues on GitHub should list some ideas.

Credits

This code is converted from the C++ sources on Chamberlain Fong's blog posts, which (I think) are based on his paper Analytical Methods for Squaring the Disc (2014).

The square image in test_images/ is https://commons.wikimedia.org/wiki/File:Graph-paper.svg and the circle is taken from Chamberlain Fong's blog posts.