Bringing Closed Polygonal Curves in the Plane to Normal Form via Local Moves

S. Avvakumov, A. Sossinsky

Research output: Contribution to journalArticlepeer-review

Abstract

We define normal forms of regular closed polygonal curves in R2, prove that any such curve can be taken to normal form by a regular homotopy, construct two different algorithms (implemented in computer animations) designed to take a given curve to normal form via local moves, present experimental results confirming that this almost always happens, and explain the biological motivation behind the algorithms, as well as their biological interpretation.

Original languageEnglish
Pages (from-to)466-473
Number of pages8
JournalMathematical Notes
Volume103
Issue number3-4
DOIs
StatePublished - 1 Mar 2018
Externally publishedYes

Keywords

  • Euler functional
  • gradient descent
  • local moves
  • normal form of a polygonal curve
  • regular closed polygonal curve
  • regular homotopy
  • winding number of a plane curve

All Science Journal Classification (ASJC) codes

  • General Mathematics

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