Constructive Whitney-Graustein theorem. Or how to untangle closed planar curves

Kurt Mehlhorn, Chee Yap

Research output: Contribution to journalArticle

Abstract

The classification of polygons is considered in which two polygons are regularly equivalent if one can be continuously transformed into the other such that for each intermediate no two adjacent edges overlap. A discrete analogue of the classic Whiney-Graustein theorem is proven by showing that the winding number of polygons is a complete invariant for this classification. Moreover, this proof is constructive in that for any pair of equivalent polygons, it produces some sequence of regular transformations taking one polygon to the other. Although this sequence has a quadratic number of transformations, it can be described and computed in real time.

Original languageEnglish (US)
Pages (from-to)603-621
Number of pages19
JournalSIAM Journal on Computing
Volume20
Issue number4
StatePublished - Aug 1991

Fingerprint

Planar Curves
Closed curve
Polygon
Theorem
Winding number
Overlap
Adjacent
Analogue
Invariant

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Constructive Whitney-Graustein theorem. Or how to untangle closed planar curves. / Mehlhorn, Kurt; Yap, Chee.

In: SIAM Journal on Computing, Vol. 20, No. 4, 08.1991, p. 603-621.

Research output: Contribution to journalArticle

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