Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-27T07:36:08.310Z Has data issue: false hasContentIssue false
  • English
  • Français

Control point insertion for B-spline curves

Published online by Cambridge University Press:  17 April 2009

Heinz H. Gonska  and
Andreas Röth
Heinz H. Gonska
Affiliation:
Dept. of Mathematics and Computer Science, Drexel University, Philadelphia, PA 19104, United States of America Fachbereich Mathematik, Universität Duisburg, D-4100 Duisburg 1, West Germany
Andreas Röth
Affiliation:
Fachbereich Mathematik, Universität Duisburg, D-4100 Duisburg 1, West Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Inserting new knots into B-spline curves is a well-known technique in CAGD to gain extra flexibility for design purposes. However, from a user's point of view, the insertion of knots is somewhat unsatisfactory since the newly generated control points sometimes show up in unexpected locations. The aim of this note is to show that these problems can be circumvented by inserting the control vertices directly, thus also providing a more natural user interface.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 2 , October 1988 , pp. 307 - 313
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Böhm, W., ‘Inserting new knots into B-spline curves’, Comput. Aided Design 12 (1980), 199–201.CrossRefGoogle Scholar
[2]Böhm, W. and Prautzsch, H., ‘The insertion algorithm’, Comput. Aided Design 17 (1985), 58–59.Google Scholar
[3]de Boor, C., A Practical Guide to Splines (Springer, New York, Heidelberg, Berlin, 1978).CrossRefGoogle Scholar
[4]de Boor, C. and DeVore, R., ‘A geometric proof of total positivity for spline interpolation’, Math. Comp. 45 (1985), 497–504.Google Scholar
[5]Cohen, E., Lyche, T. and Riesenfeld, R., ‘Discrete B-splines and subdivision techniques in Computer-Aided Geometric Design and Computer Graphics’, Comput. Graphics Image Proc. 14 (1980), 87–111.CrossRefGoogle Scholar
[8]Goldman, R.N., ‘Pólya's urn model and Computer-Aided Geometric Design’, SIAM J. Algebraic Discrete Methods 8 (1985), 1–28.CrossRefGoogle Scholar
[7]Lyche, T. and Moerken, K., ‘Making the Oslo algorithm more efficient’, SIAM J. Numer. Anal. 23 (1986), 663–675.CrossRefGoogle Scholar
[8]Marsden, M.J., ‘On uniform spline approximation’, J. Approx. Theory 8 (1972), 249–253.CrossRefGoogle Scholar
[9]Röth, A., Knoten- und Kontrollpunkteinsetzalgorthmen für B-Spline-Kurven im CAGD (Diplomarbeit, Universität Duisburg, 1987).Google Scholar
[10]Wang, Jia-ye, Wang, Guo-zhao and Peng, Qun-sheng, ‘The geometric properties and order of approximation of parametric B-splines’, (Chinese), Chinese Ann. Math. Ser A 5 (1984), 625–632.Google Scholar