Kink-free deformations of polygons

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We consider a discrete version of the Whitney-Graustein theorem concerning regular equivalence of closed curves. Two regular polygons P and P’, i.e. polygons without overlapping adjacent edges, are called regularly equivalent if there is a continuous one-parameter family Ps, 0 ≤ s ≤ 1, of regular polygons with P0 = P and P1 = P’. Geometrically the one-parameter family is a kink-free deformation transforming P into P’. The winding number of a polygon is a complete invariant of its regular equivalence class. We develop a linear algorithm that determines a linear number of elementary steps to deform a regular polygon into any other regular polygon with the same winding number.
Original languageEnglish
Title of host publicationEPRINTS-BOOK-TITLE
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Number of pages8
Publication statusPublished - 1989

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