A topological data structure for hierarchical planar subdivisions

We introduce HPS a new topological data structure that e ciently represents hierarchies of planar subdivisions thus providing direct and e cient support for GIS concepts such as abstract generalizations and multi scale partitions Unlike previous ad hoc solutions HPS provides e cient access to adjacency information for each level and across levels while storing the complete hierarchy in a single data structure without duplications HPS also provides topological oper ators that ensure global consistency Like all topological data structures HPS can be used as a framework onto which geometric and attribute information is placed HPS explicitly handles attributes consistently with modeling and naturally supports both topological and geometrical multi resolution representations We also discuss how some typical applications in GIS Digital Cartography and Finite Element mesh generation can be improved with HPS keywords topological data structures hierarchical modeling multi resolution multi scale partitions Geographic Information Systems