Bour's Minimal Surface

Click for VRML

Introduction:

Bour's minimal surface is the associated family of Bour's minimal curve. Note that the Gaussian curvature is invariant under any rotation about the z axis, even though the surface itself does not have this property.

Definition:

Note: The exponents on r are (-1 + a) and a.

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.