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On the Shape Effect of a Control Point: Experimenting with NURBS Surfaces

  • Panagiotis Kaklis
  • Spyridon Dellas

Abstract

In this paper we further the theoretical investigation, initiated in [1], on the shape effect of a single control point, measured in terms of the sign of Gaussian and mean curvatures of the underlying parametric surface. The so far obtained theoretical results are illustrated by experimenting with three typical NURBS surfaces, namely a cylinder, an ellipsoid and a torus.

Keywords

Control Point Convex Domain Parametric Point NURBS Surface Hyperbolic Domain 
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References

  1. 1.
    G.D. Koras and P.D. Kaklis, On the Local Shape Effect of a Moving Control Point, Comp. Aided Geom. Design 20 (2003) 549–562.MathSciNetCrossRefGoogle Scholar
  2. 2.
    T.G. Berry and R.D. Patterson, Implicitization and Parameterization of Nonsingular Cubic Surfaces, Comp. Aided Geom. Design 18 (2001) 723–738.MathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Franz: http://www-fourier.ujf-grenoble.fr/franz/Google Scholar
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    http://www.google.comGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Panagiotis Kaklis
    • 1
  • Spyridon Dellas
    • 1
  1. 1.Ship Design Laboratory, School of Naval Architecture & Marine EngineeringNational Technical University of AthensAthensGreece

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