基于散乱数据的二元样条S_2~1(Δ_(mn)^((2)))曲面重构方法  

Surface Reconstruction Method of Bivariate Spline S_2~1(Δ_(mn)^((2))) Based on Scattered Data

作　　者：汪春晓[1] 路游[1] 

机构地区：[1]中国石油大学(北京),北京102249

出　　处：《计算机技术与发展》2017年第8期25-29,共5页Computer Technology and Development

基　　金：国家自然科学基金资助项目(60873093)

摘　　要：在计算几何领域中,利用曲面拟合散乱数据点集,是计算机图形学以及计算机辅助几何设计中一个困难的问题。传统的基于均匀2-型三角剖分的二元样条曲面重构算法存在重构速度较慢、曲面精度不高等问题。针对上述问题,提出了一种新的曲面重构方法。该方法通过数据点构造以卷积形式表示的控制系数,并构造迭代公式,迭代计算数据点与曲面的距离,根据距离调整控制系数,直到前后两次数据点到曲面的最大距离的差值小于适当的阈值,进而确定最佳的控制系数,通过将点置于数据块中,以数据块为单位进行计算,采用取整的方式消除边界处的重复计算,减少了重构曲面的计算次数。实验结果表明,该方法提高了曲面重构的速度和质量,证明了此方法是可行、有效的。In the field of computation geometry ,the use of surface fitting scattered data points is a difficult problem for CG and CAGD. The traditional bivariate spline surface reconstruction algorithm based on uniform type-2 triangulation exists shortcomings of slow speed and poor accuracy. Aiming at these problems above, a new surface reconstruction method is developed successfully. The convolution type control coefficient is offered through the data points, and the distance between data points and surface is obtained by iterative method. Then according to the distance, control coefficient is adjusted until the difference is less than the appropriate threshold before and after the maximum distance of data points and surface, so the optimum control coefficient is determined. Then blocks are selected as basic calcula- tion unit, eliminating repeated calculation at the boundary reduced computation times. The results show that the method improves the speed and quality of surface reconstruction and is proved to be feasible and effective.

关 键 词：二元样条 卷积 曲面重构 控制系数 迭代方法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]