Nested maps---a formal, provably correct object model for spatial aggregates
Lutz Plümer, Gerhard Gröger · 1996
This paper introduces the notion of nested maps, a formal object model for the management of two-dimensional, aggregated spatial objects in a GIS.Integrity between topology and geometry of such objects can be verified with mathematical rigor.An axiomatic definition of nested maps and integrity preserving transaction rules are given.Whereas a map is a plane graph with an explicit representation of faces as its atomic areal components, nested maps are maps augmented with a recursive aggregation hierarchy.A nested map decomposes into substructures which are again nested maps.An important application is the representation of political and administrative entities and the hierarchical organization of their respective te.rritories.From a more general perspective of modeling space nested maps specify a tessellation of the plane which is most general in a precise sense.The paper provides a characterization of nested maps suitable for the representation in a computer and verifiable by automatic procedures in an efficient way.Pem,i~ion to mnke di@/h.udtopics of all or p.ti ofthis nKlteri.llfor personal or clasqroom use is granted without fee provided h-tt h copies arc r,ot made or di,&htrtcd for profit or commercial advrmtage, the coPY-,+ght notice, the title ofthe publication and its date appear.rmd notice is given that copyright is by permission of the ACM.inc.To coPY "thewise* to n:pub,is~ to pod on servers or to redistribute to list? reWir= specific penni.ssionand/or fee (;].