摘要
用提高方程阶次的方法,可以光顺和高效地反求复杂的自由型曲线曲面。基于B样条方法和贝齐尔方法逐步线性递推的性质和联系,推出了NURBS曲线插值控制顶点反求的一般算法表达式。结合边界条件,详细给出了一种四次NURBS曲线插值控制顶点反求的矩阵方程和配套算法公式。通过对涡轮增压器叶轮叶片双四次NURBS曲面的逆向重构,并将该构造曲面与双三次的构造曲面进行数据对比分析,四次构造曲线的曲率比对应的三次构造曲线的曲率,减少了36.20%;四次构造曲面高斯曲率的最大值比三次的减少了2.04%,最小值减少了99.55%,曲面的光顺性得到明显提高。研究结果证实了该矩阵方程和配套算法公式的可行性和正确性。研究结论可为工程实践中,对复杂的自由型曲线曲面的逆向重构和数字化制造,提供有效的支持和借鉴。
The complex freeform curve and surface can be smoothly and efficiently reconstructed by raising the order of equation. In this study, the general algorithm expressions for inverse computation of control vertex for NURBS curve interpolation are proposed, which is based on the property and correlation of stepwise linear recursion of B-spline method and Bezier method. One kind of matrix equation and subordinate algorithm formulae are exactly acquired for inverse computation of control vertex for quartic NURBS curve under certain boundary conditions. The bi-quartic NURBS surface of turbo impeller vane is reversely reconstructed. Compared with the cubic construction line, the curvature of the quartic construction line is decreased by 36.20%. Compared with the constructed cubic surface, the maximum Gaussian curvature of the constructed quartic surface is decreased by 2.04%, and the minimum Gaussian curvature is decreased by 99.55%. The fairness of the bi-quartic NURBS surface is improved clearly with the data comparison and contrast to the bi-cubic NURBS surface. Experimental results indicate the practicability and correctness of the matrix equation and formulae. The conclusion may provide support and reference to the digital manufacturing and reverse reconstruction of complex freeform curve and surface in practice.
作者
赵晓运
宋绪丁
Zhao Xiaoyun;Song Xuding(Ministry of Education Key Laboratory for Technology and Equipment of Highway Construction,Chang'an University,Xi'an 710064,China;School of Aeronautical Engineering(Intelligent Manufacturing),Taizhou University,Taizhou 318000,Chin)
出处
《仪器仪表学报》
EI
CAS
CSCD
北大核心
2020年第11期270-277,共8页
Chinese Journal of Scientific Instrument
基金
中央高校基金(310825163407)项目资助。
关键词
控制顶点反求
NURBS曲线插值
递推算法
叶片曲面重构
control vertex inverse computation
NURBS curve interpolation
recursive algorithm
vane surface reconstruction
