Fast partitioning of parameterized 45-degree polygons into parameterized trapezoids

In this paper, an approach to the partitioning of parameterized 45-degree polygons into parameterized trapezoids by using horizontal cuts is proposed. In the process of partitioning a parameterized 45-degree polygon, the proposed approach invokes a mixed integer linear programming solver only once and can rapidly obtain results of comparing linear expressions. Compared with previous partitioning programs, the program implementing the proposed approach is very efficient and can achieve more than 100× speed-up while partitioning large parameterized polygons or parameterized polygons with complex constraints. The approach can be used as the basis to build trapezoidal corner stitching data structures for parameterized 45-degree layouts so that models of layout-induced parasitics can be generated automatically.