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

Authors:
Alexandros I. Ginnis;E. I. Karousos;P. D. Kaklis
Affiliations:
National Technical University of Athens, School of Naval Architecture and Marine Engineering, Athens, Greece;National Technical University of Athens, School of Naval Architecture and Marine Engineering, Athens, Greece;National Technical University of Athens, School of Naval Architecture and Marine Engineering, Athens, Greece
Venue:
Computing - Geometric Modelling, Dagstuhl 2008
Year:
2009

Citing 4
Cited 0

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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.