形状调配中带参数的过渡曲线与曲面构造  

Construction of Transition Curve and Surface with a Parameter in Shape Blending

作　　者：李军成[1] 宋来忠[2] 刘成志[1] Li Juncheng Song Laizhong Liu Chengzhi(College of Mathematics and Finance, Hunan University of Humanities, Science and Technology, Loudi 417000 College of Science, China Three Gorges University, Yichang 443002)

机构地区：[1]湖南人文科技学院数学与金融学院,娄底417000 [2]三峡大学理学院,宜昌443002

出　　处：《计算机辅助设计与图形学学报》2016年第12期2088-2096,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11171181);湖南省教育厅资助科研项目(14B099)

摘　　要：针对形状调配问题中过渡曲线与曲面构造方法的不足,提出基于带参数的曲线模型构造过渡曲线曲面的方法.首先利用一类带参数的曲线模型构造一种带参数的调配函数;然后研究基于该调配函数的过渡曲线构造问题,并讨论基于能量优化法的最佳过渡曲线构造问题;最后探讨相应的过渡曲面构造问题.实例结果表明,利用带参数的调配函数构造过渡曲线曲面时,2个被过渡曲线曲面可为任意的参数曲线曲面,所构造的过渡曲线曲面不仅在边界处满足拟C2连续,而且还可通过调配函数所带的参数对其形状进行调整.In view of the deficiency of the transition curve and surface construction methods in the shape blending,a method for constructing transition curve and surface based on curve models with parameters is presented inthis paper. First, a blending function with a parameter is constructed by using a class of curve model with parameters.Then, construction of the transition curve based on the presented blending function is studied, and constructionof the optimal transition curve based on energy optimization method is discussed. Finally, constructionof the transition surface is similarly discussed. Example results show that, the two transited curves and surfacecan be arbitrary parametric curves and surfaces when the blending function is used to construct transition curveand surface. The transition curves and surfaces are not only quasi C2 continuous on the boundary, but also canachieve shape adjustment by the parameter of the blending function.

关 键 词：形状调配 调配函数 形状调整 过渡曲线与曲面 能量优化法 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]