基于预估误差补偿的NURBS曲线插补算法

任杰青; 刘凯; 赵东标

doi:10.13433/j.cnki.1003-8728.2015.0811

基于预估误差补偿的NURBS曲线插补算法

doi: 10.13433/j.cnki.1003-8728.2015.0811

1.
南京航空航天大学机电学院, 南京 210016

基金项目:

南京航空航天大学基本科研业务费项目（NS2013049）、国家自然科学基金项目（51175261）及高等学校博士学科点专项科研基金项目（20123218110020）资助

详细信息

作者简介:
任杰青（1989-），硕士研究生，研究方向为机电一体化和数控，renjieqing100@126.com

通讯作者:
刘凯，副教授，硕士生导师，liukai@nuaa.edu.cn

计量
- 文章访问数: 143
- HTML全文浏览量: 23
- PDF下载量: 6
- 被引次数: 0
出版历程
- 收稿日期: 2013-11-06
- 刊出日期: 2015-08-05

An Interpolation Algorithm for NURBS Based on Predicted Error Compensation

1.
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要: 针对传统NURBS曲线插补算法计算量大、耗时多的问题，提出基于预估误差补偿的NURBS曲线预估-校正插补算法。该算法能够以简单的线性运算代替复杂的求导运算，有效降低了计算的复杂度，提高了计算效率。并能根据曲线曲率变化趋势对预估参数值进行补偿，使预估参数值更接近实际值。为了解决传统校正公式收敛速度慢的问题，提出基于割线法的校正公式。该校正公式为超线性收敛，有效减少了迭代计算的次数。仿真结果表明：该算法的计算量小，可操作性强，稳定性好，可靠性高。能够对插补产生的速度波动进行有效控制，满足实时插补的要求。
- NURBS曲线插补 /
- 预估-校正 /
- 误差 /
- 计算效率 /
- 收敛
Abstract: The traditional NURBS interpolation algorithms are time-consuming for large amount of calculations. To solve the problem, a predictor-corrector NURBS interpolation algorithm based on predicted error compensation is presented. The interpolation algorithm avoids derivative calculation with simple linearization calculations reducing computational complexity availably and increasing computational efficiency, and also can compensate the predicted value for approaching the real value according to the changing trend of curvature. As for the slow-convergent-speed problem of the traditional corrector formula, a new corrector formula based on the secant method is presented. The new corrector formula is superlinear convergence of numerical methods reducing times of iteration effectively. The simulation experiments demonstrate that the proposed algorithm has advanced characterization of less calculations and strong maneuverability, outstanding stability and excellent reliability; it also can effectively control the rate fluctuation, and satisfy the real-time interpolation requirement.
- acceleration /
- algorithms /
- boundary conditions /
- boundary layers /
- calculations

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参考文献(15)

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