squircle 0.2.0

Stretch discs/circles into squares and squish squares into discs/circles

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 insall squircle

Usage:

from squircle import to_circle, to_square
from PIL import Image

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/

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

Squircle doesn't handle ellipses/rectangles, this more recent paper should be useful: Elliptification of Rectangular Imagery by C Fong - ‎2017

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