SuperellipseΒΆ
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A superellipse is a planar, closed curve in the rectangle . It can be viewed as a generalization of the ellipse as it retains the symmetry properties about the semi-major and semi-minor axes. All points on the curve satisfy the following equation
The ellipse is a special case of this equation with . For convex curves are obtained. Examples are the rhombus () or a curve resembling a rounded rectangle () shown below. Concave curves, like the four armed star shown below, are a result of exponents .