使用局部支撑径向基函数的隐式曲线曲面几何迭代算法  

Implicit Progressive-Iterative Algorithm of Curves and Surfaces with Compactly Supported Radial Basis Functions

作　　者：王海波 刘韬 刘圣军[1,2] 位文言 刘新儒[1,2] 刘平波[3] 白燕羽 陈月安 Wang Haibo;Liu Tao;Liu Shengjun;Wei Wenyan;Liu Xinru;Liu Pingbo;Bai Yanyu;Chen Yue’an(School of Mathematics and Statistics,Central South University,Changsha 410083;Institute of Engineering Modeling and Scientific Computing,Central South University,Changsha 410083;School of Computer and Information Engineering,Central South University of Forestry and Technology,Changsha 410004;AECC South Industry Company Limited,Zhuzhou 412000)

机构地区：[1]中南大学数学与统计学院,长沙410083 [2]中南大学工程建模与科学计算研究所,长沙410083 [3]中南林业科技大学计算机与信息工程学院,长沙410004 [4]中国航发南方工业有限公司,株洲412000

出　　处：《计算机辅助设计与图形学学报》2021年第11期1755-1764,共10页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61602524);湖南省重点研发计划(2017NK2383);中南大学研究生自主探索创新项目(2021zzts0474)。

摘　　要：由散乱数据稳定重构曲线曲面,在变分拟插值方法的基础之上,提出了使用局部支撑径向基函数的隐式几何迭代算法.首先,根据给定数据点的法向构造隐式函数的非零约束,构造计算隐函数系数的迭代格式,并讨论其收敛性;然后,在此基础上引入加速因子,对隐式迭代算法进行加速,同时讨论了加速算法的收敛性;最后,为了降低迭代过程空间和时间的复杂度,给出了一种加速算法的改进版本.数值实验表明,使用局部支撑径向基函数的隐式几何迭代算法对曲线曲面重构是有效的,并对部分信息缺失、非均匀分布、带噪声采样数据的重构也达到了较好的效果,且实现简单,易于并行.To reconstruct curves and surfaces robustly from scattered data,an implicit progressive-iterative algo-rithm with compactly supported radial basis functions based on the variational quasi-interpolation method is pro-posed.Firstly,the non-zero constraint of the implicit function is constructed using normal vectors at the given points,an iterative scheme for calculating coefficients of the implicit function is developed and its convergence is discussed.Secondly,by introducing an acceleration factor,the implicit progressive-iteration algorithm is sped up,and the convergence is analyzed.Finally,the accelerated algorithm is modified to decrease the space and time complexity.Numerical experiments show that the algorithm is effective for curve and surface reconstruction,and it also achieves good results for reconstructing from data with missing samples,non-uniform distribution,and noises.Moreover,it is simple to implement and easy to process in parallel.

关 键 词：隐式几何迭代算法 加速因子 局部支撑径向基函数 曲线曲面重构 拟插值 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]