A discrete methodology for controlling the sign of curvature and torsion for NURBS

Ginnis, A.I. and Karousos, E.I. and Kaklis, Panagiotis (2009) A discrete methodology for controlling the sign of curvature and torsion for NURBS. Computing, 86 (2-3). 117–129. ISSN 0010-485X (https://doi.org/10.1007/s00607-009-0053-8)

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Abstract

This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration.

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