The Astroidal Ellipsoid

Click for VRML

Introduction:

The astroidal ellipse is formed by cubing each coordinate in the parameterization of an ellipse. The surface above, with a = b = c, is called an astroidal sphere.

Definition:

An implicit formula for the astroidal sphere is:

Properties:

Infinitesimal Area:

The infinitesimal area of a patch on the surface is given by

dA = [click for formula]

Gaussian Curvature:

K[u, v] = [click for formula]

Gaussian curvature of the surface.

Mean Curvature:

H[u, v] = [click for formula]

Mean curvature of the surface.