Kink-free deformations of polygons

Authors:
G. Vegter
Affiliations:
Dept. of Computing Science, University of Groningen, P.O.Box 800, 9700AV Groningen, The Netherlands
Venue:
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Year:
1989

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Abstract

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, O ≥ s ≤ 1 of regular polygons with Po = 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.