Thursday, September 3, 2015

Fernandez-Guasti's squircle


In 1992, Manuel Fernandez-Guasti introduced a smooth algebraic curve that lies between the circle and the square.

The curve has two parameters: radius r and squareness s


















This is a quartic curve (i.e. degree 4) because of the x²y² term.

When s = 0, the FG-squircle is a circle with radius r.
When s = 1, the FG-squircle is a square with side length 2r.

In between, it is a shape that resembles both the circle and the square


Note: For this discussion, we shall limit the scope of the curve to
-r ≤ x ≤ r and -r ≤ y ≤ r

This quartic polynomial equation can have values for (x,y) outside this scope, but we will ignore those regions.

See http://148.206.32.135/mfg/arti/90-94/agrec-ijmest92.pdf
for Fernandez-Guasti's original paper.

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