squircle 0.0.1

squircle.py is a Python 3 utility for stretching discs/circles into squares and squishing squares into discs/circles

Usage:

from squircle import to_disc, to_square
from PIL import Image

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

there's 3 stretching methods you can choose from

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

Stretching methods

Fernández-Guasti squircle (fgs)

The Fernández-Guasti squircle (fgs) 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 allegedly difficult.

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

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

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