均匀T网格样条曲面的半规范局部细分算法  

Semi-standard Local Refinement Algorithm of Uniform T-grid Splines Surface

作　　者：胡海涛 纪小刚 张溪溪 栾宇豪 张建安 HU Haitao;JI Xiaogang;ZHANG Xixi;LUAN Yuhao;ZHANG Jian'an(School of Mechanical Engineering,Jiangnan University,Wuxi 214122,Jiangsu,China;Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology,Wuxi 214122,Jiangsu,China)

机构地区：[1]江南大学机械工程学院,江苏无锡214122 [2]江苏省食品先进制造装备技术重点实验室,江苏无锡214122

出　　处：《机械科学与技术》2021年第9期1416-1424,共9页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(51105175);江苏省“六大人才高峰”项目(JXQC-006)

摘　　要：为解决T样条曲面造型中控制点插入的半规范问题,提出了一种基于均匀T网格样条曲面的半规范局部细分算法。首先根据T样条曲面定义,将B样条曲面转换为均匀T网格样条曲面;然后在任意单一网格上进行控制点插入,或将网格进行嵌套细分。为满足曲面局部特征细分要求,建立超定方程组,用神经网络求解额外系数,添加于特定控制点上,以保证T样条曲面的半规范性;最后,通过额外系数计算新的混合函数,并构造最终曲面。并通过实例证明该算法的可行性,与现有的T样条的相比,曲面在达到相同精度时,该算法减少了多余控制点。In order to solve the semi-standard problem of control point insertion in the T-splines surface modeling,a semi-standard local refinement algorithm based on the uniform t-grid splines surface is proposed.Firstly,according to the definition of T-splines surface,B-splines surface is transformed into uniform T-grids splines surface,then control points are inserted on any single grids,and the grids can also be nested and subdivided.In order to meet the refinement requirements of local surface features,the additional coefficients need to be added to some control points to ensure the semi-standard of T-splines surface.The least square method is used to solve the extra coefficients by establishing the overdetermined equation,and the blending function of the initial uniform T-grid is transformed into the blending function of the final T-grids by the transformation matrix.The algorithm is proved to be feasible through examples.Comparing with the local refinement of T-splines surface,when the curved surface reaches the same precision,this method reduces redundant control points.

关 键 词：T样条 半规范 B样条 混合函数 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]