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.

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