The Community for Technology Leaders
RSS Icon
Issue No.06 - November (1996 vol.16)
pp: 64-71
It is well known that NURBS curves provide an exact representation of conics. Nevertheless, if this representation is exact on the geometric point of view (that is, the shape), the resulting parametrization is usually bad. For instance, the highest known continuity for a circle represented by a NURBS curve is only C1. This article presents a new reparametrization technique, called zigzag reparametrization, that improves the parametrization of a NURBS curve or surface according to a given criterion. To illustrate the technique, we study here the parametrization of the circle, but the method may be used in many other reparametrization applications.
conics, NURBS, parametrization, reparametrization
Carole Blanc, Christophe Schlick, "Accurate Parametrization of Conics by NURBS", IEEE Computer Graphics and Applications, vol.16, no. 6, pp. 64-71, November 1996, doi:10.1109/38.544074
1. L. Piegl and W. Tiller, The Book of NURBS, Springer Verlag, New York, 1995.
2. G. Farin, NURB Curves and Surfaces, A.K. Peters, Boston, 1995.
3. A. Forrest, Curves and Surfaces for Computer-Aided Design, doctoral dissertation, Cambridge University, Cambridge, U.K., 1968.
4. K. Versprille, Computer Aided Design Applications of the Rational B-Spline Approximation Form, doctoral dissertation, University of Syracuse, New York, 1975.
5. G. Farin, "From Conics to NURBS: A Tutorial and Survey," IEEE Computer Graphics&Applications, Vol. 12, No. 5, 1989, pp. 78-86.
6. L. Piegl and W. Tiller, "A Menagerie of Rational B-Spline Circles," IEEE CG&A, Vol. 9, No. 5, Sept. 1989, pp. 48-56.
7. G. Farin,Curves and Surfaces for Computer Aided Geometric Design, 3rd ed. New York: Academic Press, 1992.
8. L. Piegl, "Infinite Control Points: A Method for Representing Surfaces of Revolution Using Boundary Data," IEEE CG&A, Vol. 7, No. 3, May 1989, pp. 45-55.
9. W. Tiller, "Rational B-Splines for Curve and Surface Representation," IEEE CG&A, Vol. 3, No. 6, September 1983, pp. 61-69.
10. C. Blanc, Modélisation et Déformation des Surfaces pour la Synthése d'Images, doctoral dissertation (in French), Universitéde Bordeaux, Bordeaux, France, 1994.
11. E. Lee and M. Lucian, "Moebius Reparametrization of Rational B-Splines," Computer Aided Geometric Design, Vol. 8, 1991, pp. 213-238.
12. R. Farouki and T. Sakkalis, "Real Rational Curves are not Unit Speed," Computer Aided Geometric Design, Vol. 8, No. 2, 1991, pp. 151-158.
13. R.H. Bartels, J.C. Beatty, and B.A. Barsky, An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann, Los Altos, Calif., 1987.
16 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool