大规模散乱数据的层次B-样条曲面表示.pdfVIP

第 22 卷第 10 期 计算机学摄 Vol. 22 No. 10 1999 年 10 月 CHINESE J. COMPUTERS Oct. 1999 大规模散乱数据的层次 B- 样条曲面表示 张伟强 唐泽圣 (清华大学计算机科学与技术系 北京 100084) 擒 要 文中描述了一种大规模散乱数据的快速表示方法.该算法利用一系列从粗糙到精细的总祥条控制两格来 逐步逼近或插值给定的散乱数据点集手并且，由粗到细的细化过程只局限于误差还没有达到给定要求的区域.具体 描述了实现这种方法的 3 个关键部分 g 层次逼近、区域定拉以及 C 2 连续性的保证.文中采用一个递 !l3查找法来定 位误差大子给定凋值的区域，还利用带约束的最小二乘的方法在进行层次逼近的同时保证不同层次面片之爵的 C 2 连续性.最后，给出了该算法在实际应用中的几个实验结果. 关键词散乱数据，墨次 B- 样条，曲面拟合. 分类号: TP391 ADAPTIVE HIERARCHICAL B-SPLINE SURFACE REPRESENTAτION OF LARGE-SCALE SCATTERED DATA ZHANG Wei-Qiang TANG Ze-Sheng (De户anment 01 Computer Science and Technology , Tsinghua University, Beijing 100084) Abstract A fast algorithm for large scale scattered data interpolation and approximation is de? scribed in this paper. The representation of the large-scale scattered data is a difficult problem, especially whεn various features of the representation , such as C 2 -continuity , are required.τhe algorithm exploits a coarse-to-fine hierarchical control lattíce to fit the scattered data. and refine? ment process is only located in the regions where the error between the scattered data and the re? sult surface is greater than a specified tolerance. To ensure the C 2-continuity, a method is intro? duced to get the controllattice under constrained conditions. and the problem of continuity is con? verted into the above pr