Artifacts in Box-Spline Surfaces

  • Malcolm A. Sabin
  • Ursula H. Augsdörfer
  • Neil A. Dodgson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


Certain problems in subdivision surfaces have provided the incentive to look at artifacts. Some of these effects are common to all box-spline surfaces, including the tensor product B-splines widely used in the form of NURBS, and these are worthy of study. Although we use the subdivision form of box- and B-splines as the mechanism for this study, and also apply the same mechanism to the subdivision schemes which are not box-splines, we are looking at problems which are not specific to subdivision surfaces, but which afflict all Box- and B-splines.


Control Point Spatial Frequency Subdivision Scheme Diagonal Direction Subdivision Surface 
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  1. 1.
    Davis, P.: Circulant Matrices. Wiley Interscience, Hoboken (1979)zbMATHGoogle Scholar
  2. 2.
    Dyn, N., Gregory, J., Levin, D.: A four-point interpolatory subdivision scheme for curve design. In: CAGD, vol. 4, pp. 257–268 (1987)Google Scholar
  3. 3.
    Peters, J., Shiue, L.-J.: 4-3 Directionally Ripple-free Subdivision. ACM ToG 23(4), 980–1003 (2004)Google Scholar
  4. 4.
    Sabin, M., Barthe, L.: Artifacts in Recursive Subdivision Surfaces. In: Cohen, Merrien, Schumaker (eds.) Curve and Surface Fitting: St.Malo 2003, pp. 353–362. Nashboro Press (2003)Google Scholar
  5. 5.
    Sabin, M.: ω-convergence, A criterion for linear approximation. In: Laurent, Le Méhauté, Schumaker (eds.) Curves and Surfaces, pp. 415–420. Academic Press, London (1991)Google Scholar
  6. 6.
    Shannon, C., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press (1949)Google Scholar
  7. 7.
    Velho, L., Zorin, D.: 4-8 subdivision. In: CAGD, vol. 18, pp. 397–427 (2001)Google Scholar
  8. 8.
    Warren, J., Weimer, H.: Subdivision Methods for Geometric Design. Morgan Kaufmann, San Francisco (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Malcolm A. Sabin
    • 1
  • Ursula H. Augsdörfer
    • 1
  • Neil A. Dodgson
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridge

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