# Parametrization of distorted and dented ellipsoids

My program uses a lot of ellipsoid shaped polygons in 2 and 3 D. So far, I create them by the simple, well-known parametrization about two angles.

Now I'd like to have my ellipses a bit dented and distorted. Currently, I just need some sort of non-perfect ellipsoids, later I'd like to tune it to realisitic production defects. The ellipsoids should roughly look like they were drawn/modeled by a not-so-talented child or like they were made of thin aluminium and someone dented them with its fingers. So, the size of dents is roughly in the order of 1/10 to 1/5 of the ellipsoid size.

Are there any parametrizations to get distorted and dented ellipsoid? Or does this problem have a name to find literature about it?

• You can check some of the parametric equations in MathMod, you can check the "Holed spheres", maybe you want something like that. Here an example. – nicoguaro Jul 31 '16 at 22:28

You can distort the elliposid uniformly by applying a linear map ($\mathbf{F}$, a 3x3 matrix in 3D) such that $$\mathbf{x}_{\text{distorted}} = \mathbf{F} \cdot \mathbf{x}$$ If the map depends on position ($\mathbf{x}$) you can get more complex deformations. You could search for such maps in the literature but it will probably be easier to find what you want by trial and error.