点采样曲面的曲率估计

本文提出一种直接在点采样曲面上计算曲面的高斯曲率、平均曲率及主曲率等局部微分性质的方法。首先，为了去除测量产生的噪声和误差，引入高斯核函数为每个采样点加权；接着计算每个采样点的最近邻域点集；然后用双三次B样条曲面最小二乘拟合邻域点集，构造局部参数曲面来逼近原始曲面，以局部参数曲面的曲率估计点采样曲面的曲率；最后给出曲率估计的应用。实验结果表明，该方法能有效地反映曲面的基本特征。

Estimating curvatures for point-sampled surfaces

An approach is proposed to estimate several differential properties,including Gaussian curvature,mean curvature and main curvature on point-sampled surfaces in presence of noise.To filter out the noise and error arising out of various physical measurement processes and limitations of the acquisition technology,a Gaussian weight is assigned to each point acquired.Moving local bicubic B-spline surface is obtained by applying the least square fitting method to the nearest neighbors of the points.Then the local differential geometric properties of point-sampled surface are approximated by analyzing the bicubic B-spline surface.Applications of curvature estimation are given and experimental results are also provided.