基于空间栅格支撑与曲率云图引导的点云表面构线

Drawing Curves onto Point Clouds Based on Spatial Grid and Directed by Curvature Map

针对已有的点云表面构线方法在处理多层点云曲面模型时出现的弱鲁棒性问题,以及构线过程中缺乏直观点云形状特征引导的现象,提出一种基于空间栅格支撑与曲率云图引导的点云表面构线方法。首先,将点云划入规则分布的空间栅格并基于三参数Shepard曲面估算点云曲率;其次,依据曲率云图反映的点云几何形状特征选择构线点,并搜索沿构线点投影方向与之相交的最近非空栅格(即含有测量点的栅格),继而以最近非空栅格为中心,构建其k-最近邻域点集作为点投影算法的目标点云计算构线点的投影点;然后,插值构线点列经投影计算得到的投影点序列,获得初始曲线;最后,构造与初始曲线节点分布一致的法矢曲线作为曲线投影的方向,结合二分法与基于空间栅格支撑的点投影算法将初始曲线投影至点云曲面。实例对比表明,空间栅格的引入显著增强了点投影算法的稳定性,而曲率云图的引导则提高了用户交互选点构线过程中对点云所蕴涵形状特征的识别与分析能力。

Aiming at the current methods of drawing curves onto point clouds which are weak robustness while dealing with multi-layer point set surface models, and are lack of guiding by intuitive geometric features contained in point clouds, an approach based on spatial grid and directed by curvature map is proposed. Firstly, subdivide point clouds into spatial grids and estimate curvature based on three parameters Shcpard surface. Secondly, choose data point （point used to construct initial curve） according to geometric features illustrated in curvature image, then search the nearest non-empty grid （a grid contains at least one measured point） intersected with the projected ray started at the above data point. Subsequently, construct the k-nearest neighborhoods of the above nearest valid grid as the target point cloud surface for point projection algorithm, then calculate the projection of the chosen data point. Thirdly, interpolate each projected vertex of chosen data point to construct the initial curve. And finally, construct no rmal curve with the same knot sequences as the initial curve to determine project directions of curve, then apply binary division algorithm and projection algorithm based on spatial grids to project the initial curve onto point set surfaces. Application comparison shows that the introduction of spatial grids remarkably improves the stability of point projection algorithm, and the guidance by curvature map enhances users＇abilities of discernment and analysis of geometric features implied in point cloud surfaces.