基于十字链叉的NURBS曲面插补算法及仿真分析

针对目前曲面插补算法存在的实时性不强,插补算法需要大量的额外空间,算法步骤繁琐以及对插补过程产生的大量数据点的数据处理问题,为了保证作为数控技术核心模块的曲面插补算法的高速、高精度性能,基于德布尔递推算法思想,重新推导出了适合于曲面插补的新的NURBS曲面表达式,在此基础上重新设计了曲面插补快速算法,并着重研究了新算法的实时性.另外,为验证新算法的正确性和有效性,提出并实现了十字链叉数据表达结构,对NURBS曲面插补点微细步长及插补质量进行了分析.建立了以VC6.0/MFC为平台的、集弓高误差、速度、加速度等功能分析于一体的算法仿真验证系统,并以汽轮机叶片为例进行了验证.研究结果表明,该算法可以满足曲面插补高速、高精度的性能要求.

Simulation and analysis of algorithm for NURBS surface based on crossed orthogonal list

Aiming at the lacks of present surface interpolation algorithms, poor real-time property, more amount of extra memory, complex algorithm processes and data processing during the interpolation, and ensuring the high speed and high accuracy properties of surface interpolation algorithm which is the core function module of NC system, a new equation for NURBS that is adapted for surface interpolation was derived newly based on de-Boor recursive algorithm,then a fast interpolation algorithm for surface was developed newly, and the real-time property of the new algorithm was studied in particularly. Moreover, in order to verify the algorithm, a new data structure called crossed orthogonal list was proposed and programmed to analyze the performance of the NURBS interpolation points by the new algorithm. The analysis functions of chord error, velocity and acceleration were integrated in a simulation system based on VC6.0/MFC. Then, a turbine blade was taken for instance. The results indicate that the algorithm owns the high speed and high accuracy performance.