Superformula
Gielis superformula closed profile on the XY plane, scaled to radius. Produces a huge family of organic shapes — soft rounded stars, flower petals, squircles, astroid-like silhouettes — from just five parameters.
Node
Interactive preview is available in the interactive reader.
Sockets
center (in)- Vector3. Profile centre (default [0, 0, 0]).
radius (in)- Float. Bounding radius the shape is scaled to fit (default 10).
m (in)- Float. Number of symmetry "points" — controls rotational symmetry (default 6).
path (out)- Path — closed polyline approximating the continuous superformula.
Parameters
Segments- Number of polyline segments. Default: 256.
n1- Exponent on the primary denominator. Default: 1. Controls the overall roundness.
n2- Exponent on |cos(m·θ/4) / a|. Default: 1.
n3- Exponent on |sin(m·θ/4) / b|. Default: 1.
a- Horizontal scaling inside the cos lobe. Default: 1.
b- Horizontal scaling inside the sin lobe. Default: 1.
Reference Recipes
- Circle:
m=any, n1=n2=n3=2(Lamé's formula degenerates to a unit circle). - Soft square:
m=4, n1=n2=n3=8— a squircle. - 5-point star petals:
m=5, n1=2, n2=7, n3=7. - Spiky 6-point:
m=6, n1=0.1, n2=1.7, n3=1.7. - Astroid (hypocycloid):
m=4, n1=0.5, n2=0.5, n3=0.5.