The Sine Surface

Click for VRML

Introduction:

The sine surface is somewhat difficult to visualize, despite its simple parameterization. Unlike the cosine surface, it has a self-intersection at its center.

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:

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

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.