Introduction:
The funnel surface is the surface of revolution of the
curve log x. It can also be plotted with asymptotic curves:
Each curve on the surface of this parameterization of
the funnel either has zero curvature or has unit normals perpendicular
to the surface's normals.
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.


