Henneberg's Minimal Surface

Click for VRML

Introduction:

Henneberg's minimal surface has the interesting property that henneberg[u, v] = henneberg[-u, v + n Pi], but with an opposite orientation. Also, the surface is regular except at the points (0, n pi / 2) (Gray 692).

Definition:

Properties:

Tangent Planes:

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

[click for formula]

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:

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