- Superformula
The superformula is a generalization of the
superellipse and was first proposed byJohan Gielis .Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Others point out that the same can be said about many formulas with a sufficient number of parameters.
In
polar coordinates , with the radius and the angle, the superformula is:The formula appeared in a work by Gielis. It was obtained generalizing the
superellipse , named and popularized by Piet Hein, a Danishmathematician .Extension to higher dimensions
It is possible to extend the formula to 3, 4, or "n" dimensions, by means of
spherical product of superformulas. For example, the 3Dparametric surface is obtained multiplying two superformulas "S1" and "S2". The coordinates are defined by the relations::::where "φ" varies between "-π/2" and "π/2" (latitude ) and "θ" between "-π" and "π" (longitude ).References
*
Wikimedia Foundation. 2010.