Evolutions of planar polygons

Journal Article (Journal Article)

Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affine-invariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygonal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. In the second part, two possible polygonal analogues of the well-known Euclidean curve shortening flow are presented. The models follow from geometric considerations. Experimental results show that an arbitrary initial polygon converges to either regular or irregular polygonal approximations of circles when evolving according to the proposed Euclidean flows.

Full Text

Duke Authors

Cited Authors

  • Bruckstein, AM; Sapiro, G; Shaked, D

Published Date

  • January 1, 1995

Published In

Volume / Issue

  • 9 / 6

Start / End Page

  • 991 - 1014

International Standard Serial Number (ISSN)

  • 0218-0014

Digital Object Identifier (DOI)

  • 10.1142/S0218001495000407

Citation Source

  • Scopus