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Symmetry sets of piecewise-circular curves

Published online by Cambridge University Press:  14 November 2011

P. J. Giblin  and
T. F. Banchoff
P. J. Giblin
Affiliation:
Department of Pure Mathematics, The University, Liverpool L69 3BX, U.K.
T. F. Banchoff
Affiliation:
Department of Mathematics, Brown University, Providence, RI02912, U.S.A.
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Synopsis

Piecewise-circular (PC) curves are made up of circular arcs and segments of straight lines, joined so that the (undirected) tangent line turns continuously. PC curves have arisen in various applications where they are used to approximate smooth curves. In a previous paper, the authors introduced some of their geometrical properties. In this paper they investigate the ‘symmetry sets’ of PC curves and one-parameter families of such curves. The symmetry set has also arisen in applications (this time to shape recognition) and its mathematical properties for smooth curves have been investigated by Bruce, Giblin and Gibson. It turns out that the symmetry sets of general one-parameter families of plane curves are mirrored remarkably faithfully by the symmetry sets arising from the much simpler class of PC curves.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1135 - 1149
Copyright
Copyright © Royal Society of Edinburgh 1993

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