Connecting Polygonizations via Stretches and Twangs

We show that the space of polygonizations of a fixed planar point set S of n points is connected by O(n2 ) “moves” between simple polygons. Each move is composed of a sequence of atomic moves called “stretches” and “twangs”. These atomic moves walk between weakly simple “polygonal wraps” of S. These moves show promise to serve as a basis for generating random polygons.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Mirela Damian, Robin Y. Flatland, Joseph O'Rourke, Suneeta Ramaswami
• Keywords: Atomic Moves, CORR 2007, Education, Simple Polygons, fixed Planar Point