Convexity properties of space curves
Pages 2509 - 2517
Abstract
A set S is called convex if, for all points P, Q of S, the line segment PQ is contained in S. A simple closed planar curve and a simple closed surface are not convex by this definition, but they are called "convex" if they are boundaries of convex sets, and similarly a planar arc is called "convex" if it is a subset of the boundary of a convex set. This concept of "convexity" is ordinarily defined only for planar arcs, but we show that it can also be used in 3D. Points on the boundary of a convex set--in particular, points of a "convex" curve or surface--have useful visibility and accessibility properties. We establish some of these properties, and also characterize some special classes of "convex" space arcs and curves.
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Index Terms
- Convexity properties of space curves
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Elsevier Science Inc.
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Published: 01 November 2003
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