Symmetric Sweeping Algorithms for Overlaps of Quadrilateral Meshes of the Same Connectivity

Abstract

We propose a method to calculate intersections of two admissible quadrilateral meshes of the same connectivity. The global quadrilateral polygons intersection problem is reduced to a local problem that how an edge intersects with a local frame which consists 7 connected edges. A classification on the types of intersection is presented. By symmetry, an alternative direction sweep algorithm halves the searching space. It reduces more than 256 possible cases of polygon intersection to 34 (17 when considering symmetry) programmable cases of edge intersections. Besides, we show that the complexity depends on how the old and new mesh intersect.