Continuous and isometric deformation between catenoid and helicoid forms

An example of parametric wave generation demonstrating "Helicoid transformation", a continuous and isometric deformation of a catenoid to a helicoid such that every member of the deformation family is minimal (having a mean curvature of zero). Created on Windows using Gizmo and Igor 6.2.

The background and annotation were created using the Gizmo Annotation panel, the Tint Background panel (gradient for an empty graph), and the Gizmo Image panel (to add the graph window containing the gradient as Gizmo's background).

Each frame was created by altering a parametric wave for each frame (according to the formula on the Wikipedia page) and calling the approriate function from the Gizmo Movie procedures to add the frame to the movie.

Submitted by:

Stephen R. Chinn, Ph.D.
Night Vision and Electronic Sensors Directorate
RDER-NVS-LT
10221 Burbeck Road
Fort Belvoir, VA 22060-5806
USA

With assistance from:

Jim Prouty
WaveMetrics, Inc.