Finite element mesh generation over intersecting curved surfaces by tracing of neighbours

The use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform Boolean operations between groups of triangulated surfaces. In the intersection process, an accurate and efficient method for the determination of intersection lines is a crucial step for large scale and complex surface intersections. Given the node numbers at the vertices of the triangles, the neighbour relationship is first established. A background grid is employed to limit the scope of searching for candidate triangles that may intersect. This will drastically reduce the time of geometrical check for intersections between triangles, making the surface intersection and mesh generation a quasi-linear process with respect to the number of elements involved. The intersection lines are determined by the robust algorithm based on tracing the neighbours of intersecting triangles. In the determination of intersection between two triangles, four fundamental cases are identified and treated systematically to enhance robustness and reliability.In this paper, the consistent treatment of mesh generation along intersection lines is emphasized. The procedure ensures that all mesh generation operations are carried out on the surface concerned without leaving the surface so that elements generated will always be on the surface. Five examples on a great variety of surface and mesh characteristics are given to illustrate the efficiency and robustness of the algorithm.