Representing and processing polygonal maps with Sector Lists

In this paper we describe a novel data structure called Sector Lists (SLs) to represent discrete scalar fields equivalent to polygonal maps. The idea is to model scalar fields as a sum of elementary, wedge-shaped constant fields — what we call sectors. Sectors are organized in sorted lists in order to support an efficient processing using algorithms based on the sweeping plane paradigm. As a result, SLs combine properties often associated with rasters with those of general polygons, in the sense the borders of regions mapped to the same value can be represented exactly. Algorithms to convert, evaluate, add, transform and morph SLs are described herein, with proof-of-concept implementations publicly available. We also show how several operations commonly supported by raster and polygon-based representations can be computed with SLs. In particular, we include the results of two experiments that demonstrate the flexibility and efficiency of our prototype implementation.