An algorithm for the intersection of quadrilateral surfaces by tracing of neighbours

Abstract

The use of discrete data to represent engineering structures as derivatives from intersecting components requires algorithms to perform Boolean operations between groups of quadrilateral and triangular 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. An algorithm based on tracing the neighbours of intersecting quadrilaterals is proposed to determine the intersection lines. A background grid is employed to limit the scope of searching for candidate quadrilaterals that may intersect. This will drastically cut down the time of geometrical check for intersections between quadrilaterals, making the surface intersection and mesh generation a quasi-linear process with respect to the number of elements involved. Given the node numbers at the vertices of the candidate quadrilaterals, the neighbour relationship is then established. In the determination of intersection, each quadrilateral is divided into two triangles and four fundamental cases are identified and treated systematically to enhance robustness and reliability. Tracing the neighbours for the determination of intersection lines not only greatly increases the efficiency of the process, it also improves the reliability as branching and degenerated cases can all be dealt with in a consistent manner on the intersecting surfaces concerned. Examples on a great variety of surface and mesh characteristics are given to demonstrate the effectiveness and robustness of the algorithm.