On Normals and Control Nets

  • Ingo Ginkel
  • Jorg Peters
  • Georg Umlauf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


This paper characterizes when the normals of a spline curve or spline surface lie in the more easily computed cone of the normals of the segments of the spline control net.


Subdivision Scheme Curve Segment Spline Curve NURBS Curve Subdivision Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Boehm, W.: An affine representation of de Casteljau’s and de Boor’s rational algorithms. Computer Aided Geometric Design 10, 175–180 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Floater, M.: Derivatives of rational Bézier curves. Computer Aided Geometric Design 9, 161–174 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Floater, M.: Evaluation and properties of the derivative of a NURBS curve. In: Lyche, T., Schumaker, L. (eds.) Mathematical Methods in CAGD, Boston, Academic Press, pp. 261–274. Academic Press, London (1992)Google Scholar
  4. 4.
    Dyn, N.: Subdivision schemes in CAGD. In: Light, W. (ed.) Advances in Numerical Analysis. Volume II Wavelets, Subdivision Algorithms, and Radial Basis Functions, pp. 37–104. Oxford Science Publications, Wavelets (1992)Google Scholar
  5. 5.
    de Boor, C., Höllig, K., Riemenschneider, S.: Box splines. Springer, New York (1993)zbMATHGoogle Scholar
  6. 6.
    Boehm, W.: Generating the Bézier points of triangular splines. In: Barnhill, R., Boehm, W. (eds.) Surfaces in Computer Aided Geometric Design, pp. 77–91. North-Holland Publishing Company, Amsterdam (1983)Google Scholar
  7. 7.
    Peters, J., Shiue, L.: Combining 4- and 3-direction subdivision. ACM Transactions on Graphics 23, 980–1003 (2004)CrossRefGoogle Scholar
  8. 8.
    Loop, C.T.: Smooth subdivision surfaces based on triangles. Master’s thesis, Department of Mathematics, University of Utah (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ingo Ginkel
    • 1
  • Jorg Peters
    • 2
  • Georg Umlauf
    • 1
  1. 1.University of KaiserslauternGermany
  2. 2.University of FloridaGainesvilleUSA

Personalised recommendations