21-Oct-2019 20:30

A squircle is a shape intermediate between a square and a circle. When the squircle is centered at the origin, then a = b = 0, and it is called Lamé's special quartic. Effectively, this is still a "circle" of points at a distance r from the center, but distance is defined differently.

There are at least two definitions of "squircle" in use, the most common of which is based on the superellipse. For comparison, the usual circle is the case p = 2, whereas the square is given by the where r is the minor radius of the squircle, s is the squareness parameter, and x and y are in the interval [-r,r].

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A shape similar to a squircle, called a rounded square, may be generated by separating four quarters of a circle and connecting their loose ends with straight lines, or by separating the four sides of a square and connecting them with quarter-circles.

Such a shape is very similar but not identical to the squircle.

Although constructing a rounded square may be conceptually and physically simpler, the squircle has the simpler equation and can be generalised much more easily.

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