A subdivision algorithm for trigonometric spline curves. (English) Zbl 0984.68165

Summary: In this paper we present a subdivision algorithm for the evaluation of the trigonometric spline curves with uniform knots.


68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68W05 Nonnumerical algorithms
Full Text: DOI


[1] Cavaretta, A.; Micchelli, C., The design of curves and surfaces by subdivision algorithms, (Lyche, T.; Schumaker, L., Mathematical Methods in Computer Aided Geometric Design (1989), Academic Press: Academic Press Boston), 115-153 · Zbl 0683.65005
[2] Chaikin, G., An algorithm for high speed curve generation, Computer Graphics and Image Processing, 3, 346-349 (1974)
[3] Chui, C. K., Multivariate Splines, CBMS-NSF Regional Conference Series in Applied Mathematics (1988), SIAM: SIAM Philadelphia · Zbl 0687.41018
[4] Chui, C., Introduction to Wavelets (1992), Academic Press: Academic Press Boston · Zbl 0925.42016
[5] Cohen, E.; Lyche, T.; Riesenfeld, R., Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics, Computer Graphics and Image Processing, 14, 87-111 (1980)
[6] Dyn, N., Subdivision schemes in computer-aided geometric design, (Light, W., Advances in Numerical Analysis II, Wavelets, Subdivision Algorithms and Radial Functions (1992), Oxford University Press), 36-104 · Zbl 0760.65012
[7] Dyn, N.; Levin, D., Analysis of asymptotically equivalent binary subdivision schemes, J. Math. Anal. Appl., 193, 594-621 (1995) · Zbl 0836.65012
[8] Hoschek, J.; Lasser, D., Fundamentals of Computer Aided Geometric Design (1992), A.K. Peters: A.K. Peters Wellesley, MA
[9] Koch, P., Multivariate trigonometric B-splines, J. Approx. Theory, 54, 162-168 (1988) · Zbl 0671.41006
[10] Koch, P.; Lyche, T.; Neamtu, M.; Schumaker, L., Control curves and knot insertion for trigonometric splines, Adv. Comput. Math., 3, 405-424 (1995) · Zbl 0925.65251
[11] Lane, J.; Riesenfeld, R., A theoretical development for computer generation and display of piecewise polynomial surfaces, IEEE Transaction on Pattern Analysis and Machine Intelligence, 2, 1, 35-46 (1980) · Zbl 0436.68063
[12] Lyche, T.; Winther, R., A stable recurrence relation for trigonometric B-splines, J. Approx. Theory, 25, 266-279 (1979) · Zbl 0414.41005
[13] Lyche, T.; Schumaker, L.; Stanley, S., Quasi interpolation based on trigonometric splines, J. Approx. Theory, 95, 280-309 (1998) · Zbl 0912.41008
[14] Riesenfeld, R., Chaikin’s algorithm, Computer Graphics and Image Processing, 4, 304-310 (1975)
[15] Schoenberg, I., On trigonometric spline interpolation, J. Math. Mech., 13, 5, 795-825 (1964) · Zbl 0147.32104
[16] Schumaker, L., Spline Functions: Basic Theory (1980), Interscience: Interscience New York · Zbl 1123.41008
[17] Schumaker, L.; Trass, C., Fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines, Numer. Math., 60, 133-144 (1991) · Zbl 0744.65008
[18] Walz, G., Identities for trigonometric B-splines with an application to curve design, BIT, 37, 1, 189-201 (1997) · Zbl 0866.41010
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.