Rounded Cuboid with Superquadric Corners

The corners of the rounded cuboids on my previous post are spherical corners.

We can generalize the spherical corners (power = 2) to superquadric corners (power > 0).

Equation 1.

The equation for a rounded cuboid with superquadric corners can be given by:

       max(|x| - a, 0)^p + max(|y| - b, 0)^p + max(|z| - c, 0)^p = d^p,

where a, b, c, d ＞ 0, and p ≧ 1.

p = 1

p = 1.5

p = 2

p = 4

p = 10

Equation 2.

Furthermore, the above equation can be generalized as follows:

       max(|x| - a, 0)^p + max(|y| - b, 0)^q + max(|z| - c, 0)^r = d,

where a, b, c ≧ 0, d ＞ 0, and p, q, r ＞ 0.

Related posts:

• Equation of a Rounded Rectangle