Introduction:
The Whitney Umbrella is a wellknown example of a nonregular
surface, often referred to as a selfintersecting rectangle in three dimensions.
The end of the line of selfintersection (the "plus" shape)
is a pinch point (also called a Whitney singularity or branch point).
At a pinch point, every neighborhood of the point is selfintersecting.
Definition:
Properties:
Tangent Planes:
At u = u_{0}, v = v_{0},
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:


Mean curvature of the surface.

Surface colored by Mean curvature.


