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

A.I. Ginnis, E.I. Karousos, Panagiotis Kaklis

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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.
Original languageEnglish
Pages (from-to)117–129
Number of pages13
Issue number2-3
Early online date7 Aug 2009
Publication statusPublished - Oct 2009


  • curves
  • curvature
  • torsion
  • knot insertion

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