The Representation and Manipulation of Convex Polygons

Abstract

Many elements on printed circuit boards (pcb) and layers of very large scale integrated (VLSI) circuits are defined as polygons, possibly with curved edges. A so called 2.5D mechanical component (or ‘pockets’ therein) can be defined by a height (or depth) and a cross section, which may also be defined as a curvilinear polygonal region. Curved edges may be approximated by straight lines and concave polygons may be decomposed into constituent convex polygons. Similarly, 3D surfaces can be approximated by convex polygonal facets. Algorithms operating on convex polygons are more efficient and robust than their concave counterparts. Therefore, such algorithms are suitable for many applications in computer aided design (CAD) and manufacture (CAM).