散乱点云数据的曲率估算及应用

提出一种直接在散乱数据点云上计算曲面的局部微分性质，包括平均曲率、高斯曲率和主曲率。首先，计算各点的邻近点集，选取合适的局部基础曲面。把邻近点集投影到相应的局部基础曲面。然后，在以局部基础曲面内投影点的参数化代替空间邻近点集的参数化的基础上。用二次参数曲面逼近空间邻近点集，从而计算出各点的法矢，再对不协调的法矢方向进行调整。最后，利用曲率公式计算出各点的曲率。试验表明这种方法可以较好反映曲面的特征。运用该曲率算法对海量数据进行了简化。

Curvature Estimation of Scattered-Point Cloud Data and Its Application

A method is used to approximate several differential properties, including mean curvature, Guassian curvature and main curvature on scattered-point-sampled surfaces. Using local base surface parameterization, a parametric quadric surface approximation method is used to estimate the local surface curvature properties of scattered points based on propagating normal vector direction. The parameterization is realized by projecting data points to a local base surface. The parameters of the projected points are then used as the parameters of data points. Based on the curvature estimation, cloud data can be simplified. Experimental examples show that the algorithm is effective.