Algorithm of 2D-Voronoi diagram construction with rectangular block

Abstract

With a given set of points, Voronoi diagram is a technique of partitioning a plane into set of points having the same closest sites. A number of studies are made on the generalization of Voronoi diagram. These studies are mainly conducted on different kind of distance metric. Some studies are also made upon Voronoi diagram of sites those are not necessarily points. The current researchers present a new generalization of the construction of Voronoi diagram in the plane with axes parallel rectangles. Here, the interest has been shifted from points to simple convex orthogonal blocks i.e. rectangles. The current researchers have computed the partition of the set of the rectangles in the plane into sets of lines having the same closest sites (where sites are rectangles in the plane. This paper represents a method to find the Voronoi diagram, which considered rectangles as sites. Prototype implementation has been done and the results are quite encouraging. The algorithm is easy to implement and finds application in VLSI layouts.