一种沿公垂线方向投影的城市地下管线高效精准碰撞检测算法

An Efficient and Precise Collision Detection Algorithm for Urban Underground Pipelines Based on Projection Along Common Perpendicular

城市地下管线碰撞检测对于管线设计、管线探测、城市安全等具有重要意义。针对当前城市地下管线碰撞检测算法精度低、效率不高且较多依赖现有商用平台的问题,提出了一种沿公垂线方向投影的城市地下管线高效精准碰撞检测算法。该算法将两管段的三维空间关系归结为共面和异面两大类,当管段中心线呈现平行、共线、相交等共面空间关系时,直接利用管段中心线的几何关系及两管半径大小进行判断;当管段中心线呈现空间异面关系时,则首先沿公垂线方向进行投影变换,实现空间降维,然后结合圆与椭圆之间的最值求解方法计算管段之间的最小表面净距,从而实现精准碰撞检测。实验结果表明,该算法对三维空间管线不仅具有精准的碰撞检测结果,而且具有良好的计算效率。

Collision detection of urban underground pipelines is very significant for pipeline design, pipeline detection and urban safety. Aiming at the problems of low accuracy, inefficiency and dependence on existing commercial platforms in current collision detection algorithms for urban underground pipelines, an efficient and precise collision detection algorithm for underground pipelines is proposed, which is based on projection along common perpendicular. The algorithm classifies the three-dimensional spatial relationship between two pipe segments into two categories including coplanar and heterogeneous. When the central lines of two pipe segments are parallel, collinear or intersectant, whether they collide with each other can be easily judged through the geometric relationship of their center lines and radius size;if the central lines of pipe segments are in different planes, the projection transformation is carried out along the direction of the common perpendicular line first to reduce the spatial dimension, and then the minimum surface clearance between them is obtained through computing the maximum distance between circle and ellipse. Based on the computation above, our proposed algorithm can easily realize precise collision detection for pipelines.Experimental results show that the algorithm not only has high collision detection accuracy for three-dimensional spatial pipelines, but also has good computational efficiency.