I'm not that sure what I'll need in the further course I must say. Ellipsoids have the right visual shape for the the things I want to do right now although I might add some additional eccentricity (maybe I'm not using the terminus correctly here) in that I'll tune the equation to move the XY-Maxima along the Z-axis. Haven't really thought about that.
Additionally, mathematical-defined shapes like ellipsoids are suitable for raytracing in shaders.