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

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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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References

  1. Elber G (1992) Free form surface analysis using a hybrid of symbolic and numeric computation, Ph.D. thesis, University of Utah, Computer Science Department

  2. Farin G (2002) Curves and surfaces for CAGD. A practical guide, 5th edn. Morgan Kaufmann Publishers, San Francisco

  3. Franz M (2006) Convex—a Maple package for convex geometry. http://www-fourier.ujf-grenoble.fr/~franz/convex

  4. Gruber P (1988) Volume approximation of convex bodies by inscribed polytopes. Math Ann 281: 229–245

    Article  MATH  MathSciNet  Google Scholar 

  5. Karousos EI, Ginnis AI, Kaklis PD (2007) Quantifying the effect of a control point on the sign of curvature. Computing 79: 249–259

    Article  MATH  MathSciNet  Google Scholar 

  6. Karousos EI, Ginnis AI, Kaklis PD (2008) Controlling torsion sign. Advances in geometric modeling and processing. Lecture notes in computer science (LNCS), vol 4975, pp 92–106

  7. Lyche T, Moerken K (2004) Spline methods. Draft, Department of Informatics, University of Oslo. http://heim.ifi.uio.no/knutm/komp04.pdf

  8. Moerken K (1991) Some identities for products and degree raising of splines. Constr Approx 7: 195–208

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens, Greece

    Alexandros I. Ginnis, E. I. Karousos & P. D. Kaklis

Authors
  1. Alexandros I. Ginnis
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  2. E. I. Karousos
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  3. P. D. Kaklis
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Correspondence to Alexandros I. Ginnis.

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Communicated by C. H. Cap.

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Ginnis, A.I., Karousos, E.I. & Kaklis, P.D. A discrete methodology for controlling the sign of curvature and torsion for NURBS. Computing 86, 117–129 (2009). https://doi.org/10.1007/s00607-009-0053-8

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  • DOI: https://doi.org/10.1007/s00607-009-0053-8

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