Research On Algorithm Of Discrete Curvature Based On Triangular Mesh

With the rapid development of 3D optical measurement technology,3D laser scanner is widely used in many fields, such as aerospace, automobile, household appliances, clothing and shoes,furniture, toys, medical repair, cultural relic repair, archaeology and criminal investigation, the process of large-scale scattered data becomes more and more important.Among these point cloud data smoothing and decimation have been the hot point in the recent years. Many curvature algorithms of point cloud have the problems with accuracy and stability, this thesis mainly studies the algorithm in order to solving the problems, then the improved curvature algorithm of point cloud is applied to the actual scanning point cloud smoothing of measured data.This thesis based on differential geometry systematically researches the estimation algorithm of point cloud discrete curvature.By sampling data of spherical surface, cylindrical surface and saddle surface, and using the results calculated by theoretical algorithm to compare with the results calculated by classic point cloud curvature algorithm, it shows that the mainstream algorithm of discrete curvature used for data processing has large difference and it is not stable.This thesis is based on discrete point cloud-generated model. First of all, it defines cosine differences of the maximum corner and minimum corner of the triangle to be the determining factor of the triangle regularity. By using spherical surface to be the sampling object, by Mayer algorithm it can work out the error of discrete curvature in different neat degree of the triangular patch, and sampling the different sampling interval of saddle surface, by calculating the error of discrete curvature and comparison, it can analyze the influence of sampling interval on discrete curvature. This thesis improves the area calculation of Voronoi area, designs and makes an improved algorithm based on Mayer algorithm through the neat degree of the triangular patch, and apply it to curvature algorithm of spherical surface, cylindrical surface and saddle surface. The results present that this algorithm has improved the accuracy and stability of discrete curvature of scattered point cloud effectively.The improved algorithm is applied to the smoothing of practical scanning measurement data. Through the analysis of the local shape features of scattered point cloud data to explore an algorithm of point cloud smoothing, which is based on the analysis scattered point cloud data.The algorithm uses average curvature threshold to extract the edge feature points and noise points of large curvature and rapidly identify the feature points of point cloud data.The results present that after smoothing, the sudden changes of curvature caused by noise data are effectively inhibited,and the curvature of point cloud data transmits smoothly. The results indicate that this algorithm can not only recognize the edge contour and the characteristics of the shape well but also reach the goal of smoothing on the premise of keeping shape and features.The results of the thesis have been integrated with the self-development 3D laser scanning measurement software. The curvature algorithm of point cloud is applied to the actual scanning point cloud smoothing of measured data.They have solved the problems of smoothing and decimation better. The research is recognized by the enterprise, and it is helpful to the promotion of laser scanning technology.