Superformula - Polar Equation


The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. The upcoming computer game No Man’s Sky heavily employs the superformula for the procedural generation of its digital universe.

The formula was obtained by generalizing the superellipse, named and popularized by Piet Hein, a Danish mathematician.

Related formulas


r(ϕ)radius (dimensionless)
mgeometric parameter (dimensionless)
ϕangle (dimensionless)
ageometric parameter (dimensionless)
n2geometric parameter (dimensionless)
bgeometric parameter (dimensionless)
n3geometric parameter (dimensionless)
n1geometric parameter (dimensionless)