An algorithm for resizing polygonal regions and its applications to LSI mask pattern design

In this paper we consider the problem of resizing figures in a digitized XY coordinate plane. the figures are regions closed by line segments parallel to the × or Y axis or line segments at 45° angles to the axes. By resizing we mean that, given the closed regions and a change width, we expand or contract the input regions by the change width. After first proving some theorems on resizing, we propose an algorithm solving the problem in running time 0 (n log n), where n is the number of vertices in the regions. For particular applications we consider examples using the algorithm for verifying compliance with design rules for the smallest feature size and spacing in a mask pattern, and also the compensation for characteristic machine error in pattern generators, apertures, etc.