膜结构三角网格模型短程线的快速生成算法

A fast algorithm for geodesic in triangular mesh models of membrane structures

以短程线作为膜片的边界进行裁剪可以大幅节省膜材,以短程线方式在气承式膜结构上布置交叉索网可以最大限度提高充气膜结构的承载能力.本文提出一种快速稳定的短程线生成算法.该算法与传统的短程线算法不同之处在于,不是通过反复计算空间上的最短路径来获得,而是把空间问题转换为平面问题,在平面上找到连接两点的最短路径(即直线),再根据映射关系转换到三维空间曲面上,从而找到空间上的短程线.通过实际工程验证,本文算法能快速稳定地生成短程线.

Geodesic lines can be used as borderline of membrane surface in cutting pattern analysis to yield substantial savings in membrane materials. In addition, setting cross cable network on an air-supported structure based on the geodesic line can maximize the structure＇s load-carrying capacity. A new fast and stable algorithm generating geodesic lines is put forward in tbis paper. 11 differs from traditional geodesic line generating algorithm in no need to repeatedly calculate the shortest path in three-dimensional （3D） space. On the contrary, the problem is transformed from 3D space to 2D plane to find the shortest path,which is the straight line in the 2D plane. Then geodesic lines in the 3D space can be found according to the mapping relation. The new algorithm has been proved to be a fast and stable algorithm for geodesic by successful application in practical engineering.