基于Newton-Rapson迭代法的NURBS插补算法的研究  

Research on NURBS interpolation algorithm based on Newton-Rapson iteration method

作　　者：张万军 张峰[1,3] 张景轩 张景怡 张景妍 许冬梅 

机构地区：[1]泉州信息工程学院,福建泉州362000 [2]西安交通大学机械工程学院,西安710049 [3]兰州工业化设备有限公司,兰州730050

出　　处：《工业仪表与自动化装置》2017年第5期7-12,共6页Industrial Instrumentation & Automation

基　　金："高档数控机床与基础制造装备"科技重大专项(2016ZX040001-181);国家自然科学基金(51165024)

摘　　要：一阶、二阶Taylor展开式求解NURBS曲线插补坐标点ui+1,存在计算量大、插补时间长等问题,该文提出了一种基于Newton-Rapson迭代法的NURBS插补算法。仿真和实验结果表明:该算法计算过程简单有效,具有可行性和实用性,可以减少插补计算量和插补时间,提高插补精度和加工效率,满足了数控系统实时、高速、高效率插补的要求,对其他数控插补的过程具有很强的借鉴意义。When the coordinate point ui ＋1 of NURBS curve interpolation is solved with Taylor first-order and second-order expansions, there are some problems of large computation complexity and long interpolation time. A NURBS interpolation algorithm based on Newton-Rapson iteration method is pro-posed in this paper. The simulation and experimental results show that the proposed algorithm is simple and effective, and it can reduce the interpolation computation complexity and interpolation time to im-prove the interpolation precision and processing efficiency and meet the requirements of real-time, high-speed and high-efficiency interpolation of CNC system. This algorithm is feasible and practical and it has reference significance to other CNC interpolation.

关 键 词：NURBS曲线 插补算法 Taylor展开式 Newton-Rapson迭代法 实时插补 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] TP391[自动化与计算机技术—控制科学与工程]