Superellipsoid
A shape that morphs continuously from cube to ellipsoid to concave star through two exponents.
Superellipsoid morphs continuously between a cube, an ellipsoid and a concave star through two exponents. It is the quickest way to a rounded cube driven by one parameter.
Geometry
Follows Barr's parametric definition. The topology is the same ring grid as Sphere (single vertex at each pole), while the size is set per axis with Width, Depth and Height.
Roundness 1 (ε1) is the exponent of the vertical profile; Roundness 2 (ε2) is the exponent of the horizontal section.
| Roundness | Result |
|---|---|
| 0.01 | close to a cube |
| 0.3 – 0.5 | rounded cube |
| 1 | ellipsoid (sphere) |
| 2 | octahedron-like |
| 3 – 4 | concave star |
The pivot is at the bottom, so a shape of height h occupies y=0 to y=h.
Parameters
| Label | Script key | Default | Range | Description |
|---|---|---|---|---|
| Width | w | 1 | 0.01 ~ 1000 | Size along local X, in meters |
| Depth | d | 1 | 0.01 ~ 1000 | Size along local Z, in meters |
| Height | h | 1 | -1000 ~ 1000 | Size along local Y, in meters |
| Roundness 1 | e1 | 1 | 0.01 ~ 4 | Vertical profile exponent (ε1) |
| Roundness 2 | e2 | 1 | 0.01 ~ 4 | Horizontal section exponent (ε2) |
| Segments | seg | 24 | 3 ~ 128 | Divisions around the shape |
| Rings | rings | 12 | 2 ~ 128 | Bands along the height |
The two exponents are independent. Lowering only ε1 approaches a flat-topped cylinder; lowering only ε2 gives a column with a square section.
How to create
-
Drag in empty space to set the footprint (Width × Depth).
-
Click to confirm, then move the mouse up to set the Height.
-
Click again to finish, then dial in the exponents in the Inspector.
Scene view editing
The X, Z and Y handles drive Width, Depth and Height. Roundness is slider-only — drag it and watch the form change live.
Tips
For a rounded cube, Superellipsoid with Roundness 0.3–0.5 beats Box + Bevel — one parameter controls the fillet.
Above Roundness 2 the surface goes concave and polygons crowd together; raise Segments and Rings to keep the form readable.
Script
In a script this shape is written as superellipsoid.
superellipsoid "RoundedCube" w=1 d=1 h=1 e1=0.4 e2=0.4 @0,0,0
superellipsoid "Star" w=1 d=1 h=1 e1=3 e2=3 seg=48 rings=24 @2,0,0
See also — Shape Type List · Creating Shapes and Modes · Scene Script Syntax