Superellipse

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Superellipse

In: Mathematics

Ellipses can be defined analytically as the collection of points (x,y) that satisfy the equation

(x/a)^2 + (y/b)^2 = 1,

where a and b are just some positive constants. Each distinct ellipse can be created by simply picking the right values for a and b.

Superellipses are just like ellipses, except that the exponent in the equation isn’t necessarily 2. That is, a superellipse is the collection of points (x,y) that satisfy the equation

|x/a|^n + |y/b|^n = 1,

where a, b, and n are positive constants. When n=2, the superellipse equation is equivalent to the ellipse equation, so ellipses are just a special case of superellipses.