Superquadrics ↩

shorthands: {"sq": "superquadric", "Sq": "Superquadric"}
aliases: [Super-quadrics, Superquadratics]
created: 2021-12-17 13:22:56
modified: 2022-04-19 13:12:24

The following parameters are used here (This is the way they are parameterized in LIGGGHTS as well.^[Podlozhnyuk, A., Pirker, S., & Kloss, C. (2017). Efficient implementation of superquadric particles in Discrete Element Method within an open-source framework. Computational Particle Mechanics, 4(1), 101–118. Link
]):

• Blockiness 1:
• Blockiness 2:
• Half-length along the axis:
• Half-length along the axis:
• Half-length along the axis:

When , we get an ellipsoid.

Parametrization

We can parameterize a superquadric's surface with the coordinates and the following way:

Normal vectors

The normal vectors of the surface in a point described by the coordinates:

Inverse parametrization

Let's say we have a point near the surface of the shape. We can get it's coordinates the following way: