Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Davis, P.: Circulant Matrices. Wiley Interscience, Hoboken (1979)
Dyn, N., Gregory, J., Levin, D.: A four-point interpolatory subdivision scheme for curve design. In: CAGD, vol. 4, pp. 257–268 (1987)
Peters, J., Shiue, L.-J.: 4-3 Directionally Ripple-free Subdivision. ACM ToG 23(4), 980–1003 (2004)
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)
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)
Shannon, C., Weaver, W.: The Mathematical Theory of Communication. University of Illinois Press (1949)
Velho, L., Zorin, D.: 4-8 subdivision. In: CAGD, vol. 18, pp. 397–427 (2001)
Warren, J., Weimer, H.: Subdivision Methods for Geometric Design. Morgan Kaufmann, San Francisco (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sabin, M.A., Augsdörfer, U.H., Dodgson, N.A. (2005). Artifacts in Box-Spline Surfaces. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_21
Download citation
DOI: https://doi.org/10.1007/11537908_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28225-9
Online ISBN: 978-3-540-31835-4
eBook Packages: Computer ScienceComputer Science (R0)