×

Conditions for regular \(B\)-spline curves and surfaces. (English) Zbl 0755.41009

A curve with \(C^ 1\) components is said to be regular if it has a continuous unit tangent and if it has no self-intersections. In the paper under review the new sufficient conditions for the regularity of a B- spline curve in \(\mathbb{R}^ d(d>1)\) are derived. Extensions to tensor product B-spline surfaces are also discussed.

MSC:

41A15 Spline approximation
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] C. DE BOOR, (1978), A Practical Guide to Splines, Springer-Verlag. Zbl0406.41003 MR507062 · Zbl 0406.41003
[2] H. EDELSBRUNER, (1987), Algorithms in combinatorial geometry, Springer-Verlag. Zbl0634.52001 MR904271 · Zbl 0634.52001
[3] J. M. LANE and R. F. RIESENFELD (1980), A theoretical development for the computer génération and display of piecewise polynomial surfaces, IEEE T. Pattern Anal. 2, 35-46. Zbl0436.68063 · Zbl 0436.68063 · doi:10.1109/TPAMI.1980.4766968
[4] K. H. LAU, (1988), Conditions for avoiding loss of Geometric continuity on spline curves, Comput, Aided Geom. Design. 5, 209-214. Zbl0646.41009 MR959605 · Zbl 0646.41009 · doi:10.1016/0167-8396(88)90004-0
[5] C. M. STONE and T. DEROSE, (1989), A geometric characterization of parametric cubic curves, ACM Trans. Graph. 8, 147-163. Zbl0746.68102 · Zbl 0746.68102 · doi:10.1145/77055.77056
[6] C. Y. WANG, (1981), Shape classification of the parametric cubic curve and parametric B-spline cubic curve, Comput. Aided Design. 13, 199-206.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.