SuperEllipsoid¶

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A SuperEllipsoid is a solid with the bounding box $[-R_x,R_x]\times\in [-R_y,R_y]\times\in [-R_z,R_z]$ . It can be viewed as a generalization of an ellipsoid. All points on the surface satisfy the following equation:

$\begin{eqnarray*} \left(\Big\vert \frac{x}{R_x} \Big\vert^{\tfrac{2}{e}} + \Big\vert \frac{y}{R_y} \Big\vert^{\tfrac{2}{e}}\right)^{\tfrac{e}{n}}+ \Big\vert \frac{z}{R_z} \Big\vert^{\tfrac{2}{n}} = 1 \end{eqnarray*}$

The ellipsoid is a special case of this equation with $n=e=1$ as are cubes and cylinders.