基于改进 Voronoi 区域面积的 Mark Meyer 曲率估算方法

摘要

以微分几何曲率计算公式为理论基础，对常用的Mark Meyer离散点云曲率估算方法进行改进，提出基于Voronoi区域面积的改进Mark Meyer算法。针对Mark Meyer算法中Voronoi区域面积的计算进行改进，对于Voronoi区域中存在钝角的情形进行详细论述并且改进钝角三角形的计算公式，同时给出更为准确的面积计算方法。将该算法应用于球面、柱面、抛物面、马鞍面，计算结果表明该算法提高了离散点云曲率估算的精度和稳定性。%Taking on the calculation formula of differential geometric curvature as theoretical foundation , Mark Meyer ’ s estima-tion methods of discrete point cloud curvature are improved , the thesis puts forward an improved Mark Meyer algorithm on the ba-sis of Voronoi area .The calculation of Mark Meyer algorithm on the basis of Voronoi area is improved , the existence of an obtuse angle in Voronoi area situation is discussed in detail and the formula of the obtuse triangle is improved , at the same time , it gives a more accurate method of calculating the area .The algorithm is applied in spherical , cylindrical, parabolic, saddle surface.The calculation results show that this algorithm enhances the estimation accuracy and stability of discrete point cloud curvature .