点云模型上测地线的计算

给定点云模型上2点，将点云数据沿与xyz三坐标轴垂直方向进行单元剖分后，采用Dijkstra算法求出2点间的最短路径作为初始测地线；然后通过带弧长最短约束的平方距离最小化方法对初始测地线进行迭代优化，计算得到点云模型上给定2点间的一条样条表示的精确测地线．文中算法只需局部拟合抛物曲面，无需对点云模型进行三角化或曲面重建，适合大规模点云数据模型上测地线的计算．

Computing Geodesics on Point Clouds

Given two points on an object represented by point cloud, we first obtain an approximately shortest path between the two points as an initial active curve by using Dijkstra's algorithm, then we use square distance minimization method to compute the active curve iteratively to be the geodesic between the two points on the point cloud. We define the objective function to be constraints of the distance between the active curve and the point cloud as well as the arc length of the active curve, and then minimize the objective function step by step by relocating the control points of the active curve until a convergence result is achieved. The method avoids triangulating or reconstructing the point cloud to be a surface model so that it is practicable for dealing with the point cloud with a huge number of scattered points.