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.