Disk Flow Applets 
Written by Rick Vaughn

Based on the work of Dr. Joel Hass and Dr. Peter Scott.

LINKS

  1. Disk Flow main version
  2. Rectangular Disk Flow
  3. Convex Hull Flow
  4. Two Curves Flow
  5. New Inner Flow (In progress)



Information about the disk flow
The disk flow applet implements a version of a curve shortening algorithm that appeared in the paper "Shortening Curves on Surfaces" by Joel Hass and Peter Scott. This article can be found in Topology Vol. 33, No. 1, pp. 25-43, 1994.
The disk flow algorithm curve shortens a curve on a surface by covering it with a sequence of convex disks and replacing the portion of the curve inside of each disk with the unique geodesic segment that preserves the end points. In this application, the surface is a plane and so the geodesic segments are all line segments. The sequence of disks used is a grid of squares. The curve is shortened by replacing the portion of the PL curve inside each square with a line segment inside that same square that preserves the end points. The new PL curve therefore has its vertices on the current grid of squares. The grid is then shifted by a third and the process is repeated.