摘要
基于NURBS曲线导矢的计算公式,首先给出了平面NURBS曲线精确等距线的生成算法,这种算法稳定可靠、计算精度高,但其缺点是计算过程中有可能出现自交;针对这种情况,进一步给出了等距线生成的改进算法,这一算法可有效去除等距曲线的自交,并降低求交计算的复杂度。在以上两种算法的基础上,通过在NURBS曲线的精确等距线上采样有限个数据点,利用NURBS曲线的反算,完成了NURBS等距曲线的有理逼近;算法所得的等距逼近曲线仍具有NURBS形式,便于保持造型系统中数据结构的统一。最后在C++Builder开发环境下实现了算法的仿真验证,在CAD/CAM/CAGD中具有很高的实用价值。
Firstly, based on the derivatives of NURBS curve, it presents the generation algorithm of offset curve. This algorithm is stable, reliable and accurate, but it exists self-intersection problems in the offsetting computation. For this situation, the improved algorithm of offset curve is proposed. This algorithm can well process self-intersection problems and reduce computational complexity of intersection calculation. On the basis of the above two algorithms, through sampling limited data points on offset curve, it completes the rational approximation of offset curve based on NURBS curve inverse algorithm. The approximating curve is still a NURBS rational polynomial form This makes it easy to maintain the unity of data structure in modeling system. Finally, the simulation process of algorithms are applied in practical system based on C ＋＋ Builder development environment, which has a high practical value in the CAD/CAM/CAGD.
出处
《机械设计与制造》
北大核心
2014年第7期224-227,共4页
Machinery Design & Manufacture
基金
国家自然科学基金资助项目(51375285)
