The quad view data structure — a representation for planar subdivisions

Abstract

Applications in cartography, computer graphics and computer aided engineering require the representation and manipulation of planar subdivisions. Topology-oriented approaches represent the relations existing between the vertices, edges and faces of a planar subdivision. We extend this standard approach by decomposing the faces into trapezoidal views. By defining a neighborhood relation among the views we obtain the view graph which forms the basis of the quad view data structure — a new data structure for representing planar subdivisions. We present some basic operations on this data structure, and we show how it can be used to traverse a planar subdivision. Furthermore we sketch an algorithm for overlaying planar subdivisions represented by the quad view data structure. This algorithm is optimal for simply connected planar subdivisions: its time and storage requirements are linear in the size of the output subdivision. Finally we apply this overlay algorithm to implement locational vector-based map overlay operations.