基于径向基函数的离散数据重建方法

摘要

针对离散数据的曲面拟合问题,提出一种基于八叉树分割的径向基函数曲面拟合方法.通过对给定的曲面点集构造相应的离面约束点集及对应非零函数值,对包含所有曲面约束点和离面约束点的点云数据进行八叉树空间分割,然后在八叉树分割的每个叶结点建立相应的方程组并求解,从而构造出插值或逼近属于该叶结点的数据点的三次样条径向基函数,最后提取该基函数的零等值面,并绘制得到最终的重建曲面.方法较好的解决了离散数据插值和拟合的计算速度和稳定性问题.%Aiming at the surface fitting of the scattered data, this paper proposes a fitting method of curved surface based on the radial basis functions of octree space partition.lt partitions the point-cloud data space firstly and creates octree topologic structure accordingly through given surface point sets.Then,at each cell of the octree partitions,a radial basis function that interpolates or approximates the data points which belong to the current cell is created. This method is a good solution for the numerical instability and computing speed of scattered data interpolation and fitting.