Supershape / 01

The superformula

Geometry

Johan Gielis' superformula (2003) generalises the circle, ellipse and superellipse. In polar form:

r(θ) = ( |cos(mθ/4) / a|ⁿ² + |sin(mθ/4) / b|ⁿ³ )^−1/n1

A 3D supershape is the spherical product of two such curves — a section r_ϑ(θ) and a profile r_φ(φ):

x = r_ϑ cos θ · r_φ cos φ
y = r_ϑ sin θ · r_φ cos φ
z = r_φ sin φ

m sets the rotational symmetry; n1, n2 and n3 control roundness, pinching and spikiness; a and b stretch the axes.

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Shape & appearance

Section ϑ

m n1 n2 n3 a b

Profile φ

m n1 n2 n3 a b

Appearance

Resolution Surface colour Rendering Auto-rotate

Saved PNGs

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