基于散乱数据的层次B样条曲面重构与优化

运用B样条曲面的表示方法，构造了初始B样条曲面网格控制点逼近散乱点集，在此基础上构造包围盒进行局部搜索，用于误差检测，将查找问题转化为计算问题；并采取单元凝聚方式处理小单元，减少了误差超限的子区域个数，最后在误差超限的子区域内优化曲面.由粗糙到精细，实现了散乱数据的曲面重构与优化.该方法在误差检测和区域处理上进行修正，从而加快了搜索速度，简化了计算.算例表明，算法简单易行，逼近效果良好.

Surface Reconstruction and Optimum of Hierarchy B-Spline Based on Scattered Data

By using the algorithm of B-spline surface representation,initial B-spline surface control lattice was constructed to approach scattered data sets at first,on the basis of which the bounding box was designed to search locally and to detect the error,and to transfer finding problem into computing problem.To deal with small elements via element condensation,the regional numbers of the exceeding errors are reduced and surface is optimized in the region of the exceeding errors,then surface reconstruction and its optimization are realized from coarse to fine.The algorithm is modified in the error detection and regional processing so that the searching is more quick and computing is simplified.Thus the speed has been quickened and the computing is much easier.It is also proved that the computing is easy and feasible to make,and the approximating effect is quite good.