A shift-add algorithm for generating B-spline

• Autorzy: Gu F.
• Języki publikacji: EN

Abstrakty

EN

A CORDIC- based shift-add algorithm for generating B-spline curves is presented in this paper. This algorithm can be realized by hardware without multiplier, or coded with assembly language and run inthe basic computing system which exists in many application systems. Convergence of the algorithm was proved. Errors were estimated and well controlled in the algorithm. A numerical experiment was carrierout to validate algorithm. This algorithm can be used for adding complex curve plotting functions in embedded systems.

Słowa kluczowe

EN

B-spline; CORDIC; basic computing system; shift-add algorithm

PL

krzywa sklejana; CORDIC; podstawowy system komputerowy

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2013
• Tom: Vol. 20, no. 4
• Strony: 271--278
• Opis fizyczny: Bibliogr. 10 poz., tab., wykr.

Twórcy

autor

Gu F.

• Zhejiang Technical Institute of Economics, Hangzhou 310018, China 66 Xuezheng St., Xiasha, Hangzhou, Zhejiang, China

Bibliografia

• [1] G. Aumann. Corner cutting curves and a new characterization of B´ezier and B-spline curves. Computer Aided Geometric Design – CAGD, 14(5): 449–474, 1997.
• [2] C. de Boor. Splines as linear combinations of B-splines, Approximation Theory II, G.G. Lorentz, C.K. Chui and L.L. Schumaker [Eds.], pp. 1–47, Academic Press, New York, 1976.
• [3] C. de Boor, K. H¨ollig. B-splines without divided differences, in Geometric Modeling, G. Farin [Ed.], SIAM, pp. 21–27, 1987.
• [4] GU Feng. Convergence and Error Estimation of Coordinate Rotating Algorithm and Its Expansion. Chinese Journal of Numerical Mathematics and Applications, 28(2): 1–9, 1987.
• [5] J.E. Volder. The CORDIC Computing Technique, IRE Transactions on Electronic Computers, EC-8(9): 330–334, 1959.
• [6] J.M. Muller. Elementary Functions, Algorithms and Implementation, Birkhauser Boston, 1st edition, 1997. 2nd edition, 2006, pp. 133–156.
• [7] N. Eklund. CORDIC: Elementary Function Computation Using Recursive Sequences. International Conference on Technology in Collegiate Mathematics (ICTCM), 11, 1998.
• [8] R. Andraka. A Survey of CORDIC Algorithms for FPGA Based Computers. Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays (FPGA), pp. 191–200, 1998.
• [9] W. Bohm, G. Farin, J. Kahmann. A survey of curve and surface methods in CAGD, Computer Aided Geometric Design, 1: 1–60, 1985.
• [10] X. Hu, R. Harber, S. Bass. Expanding the Range of Convergence of the CORDIC Algorithm. IEEE Transactions on Computers, 40: 13–21, 1991.