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IJMERR 2022 Vol.11(7): 549-555

Analysis and Optimisation Strategy on Influence of Knot Vector to NURBS Curve

Zheng Shuai 1, Wang Xingbo1, and Yan Jihong2
1. Department of Mechanical Engineering, Foshan University, Foshan, China
2. GSK CNC EQUIPMENT CO., LTD, Guangzhou, China

Abstract—This study investigates the variation in the NURBS shape caused by knot vectors produced by various algorithms to minimise the influence of knot vectors on the NURBS interpolation. The differences in shape variations of NURBS curves computed by knot vectors generated by the Hartley–Judd, Riesenfeld and Rogers algorithms are compared and analysed; an error function is defined to analyse the mathematical features of the differences caused by the three calculations and a weighted average calculation method beyond the classical algorithm is proposed. Additionally, the study introduces a combinatorial algorithm for optimising the computing process and increasing computing efficiency. The experimental results show that the new method produces a more accurate NURBS curve than the classical method does, making it more suitable for CNC interpolation.

Index Terms—CNC interpolation, NURBS, Knot vector, Error analysis

Cite: Zheng Shuai, Wang Xingbo, and Yan Jihong, "Analysis and Optimisation Strategy on Influence of Knot Vector to NURBS Curve," International Journal of Mechanical Engineering and Robotics Research, Vol. 11, No. 7, pp. 549-555, July 2022. DOI: 10.18178/ijmerr.11.7.549-555

Copyright © 2022 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.