基于4D Shepard 曲面的点云曲率估算

为了高效处理大规模点云数据，提出了一种新的曲率估算方法.该方法基于空间六面体栅格分割点
云，针对每个栅格中的测量点逼近局部二次抛物面，通过计算并检查抛物面的最小采样密度和自适应划分
栅格来构建符合给定允差的局部曲面，使用步进法对曲面进行采样，利用坐标转换法计算每个采样点的曲
率、插值采样点的坐标和曲率来构造全局4D Shepard 曲面，并快速计算点云中每个测量点的曲率.结果表
明，该方法通过Shepard 曲面插值点的简单线性组合估算曲率，无需构建三角网格，具有复杂度低，实用
性强的特点.应用该方法能够快速、准确地获取大规模离散数据的曲率值.

Efficient curvature estimation based on 4D Shepard surface

To deal with a large number of measured points effectively, a new curvature estimation method based on global 4D surface was proposed. The method subdivided point cloud into many cubic grids, and then fitted a local parabolic surface to the points in each grid within a given tolerance. The local surface was sampled by marching method, and the curvatures of the sampled points were estimated by coordinate transformation method. After a global 4D Shepard surface over these sampled points was interpolated , the curvature of each point in the point cloud was calculated. Results show that compared with previous methods, the efficiency of this method is higher for avoiding triangulation of point cloud and using a global model but thousands of local surface patches. The method can be applied to many fields including visual reality, computer vision and reverse engineering.