
Evolutions of planar polygons
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.
Duke Scholars
Altmetric Attention Stats
Dimensions Citation Stats
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Artificial Intelligence & Image Processing
- 1702 Cognitive Sciences
- 0801 Artificial Intelligence and Image Processing
Citation

Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Artificial Intelligence & Image Processing
- 1702 Cognitive Sciences
- 0801 Artificial Intelligence and Image Processing