The Ellipsoid

Click for VRML

Introduction:

The ellipsoid is so called because its cross sections parallel to the xy, xz and yz planes are all ellipses. It has the interesting property that it is regular everywhere except at the north and south poles. Note also that its parameterization looks much like that of a sphere, but stretched by the constants a, b and c in the x, y and z directions.

Definition:

Properties:

Tangent Planes:

At u = u0, v = v0, the tangent plane to the surface is parameterized by:

Infinitesimal Area:

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

Gaussian Curvature:

Gaussian curvature of the surface.
Surface colored by Gaussian curvature.

Mean Curvature:

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

Mean curvature of the surface.
Surface colored by Mean curvature.