Partitioning parameterized 45-degree polygons with constraint programming

Abstract

An algorithm for partitioning parameterized 45-degree polygons into parameterized trapezoids is proposed in this article. The algorithm is based on the plane-sweep technique and can handle polygons with complicated constraints. The input to the algorithm consists of the contour of a parameterized polygon to be partitioned and a set of constraints for parameters of the contour. The algorithm uses horizontal cuts only and generates a number of nonoverlapping trapezoids whose union is the original parameterized polygon. Processing of constraints and coordinates that contain first-order multiple-variable polynomials has been made possible by incorporating the JaCoP constraint programming library. The proposed algorithm has been implemented in Java programming language and can be used as the basis to build the trapezoidal corner stitching data structure for parameterized VLSI layout masks.