Friday, October 21, 2016

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 = dp,

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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