TOPOLOGICAL MODELS FOR 3D SPATIAL INFORMATION SYSTEMS Simon Pigot, Environmental Systems Research Institute, 1 380 New York St., Redlands, Ca. 92373 email: uucp: uunet!esri!atlas!simon internet: spigot@esri.com Abstract The need for complex modelling and analysis of 3-dimensional data within a spatial information system (SIS) has been established in many fields. While much of the data that is currently being modelled seems to require "soft-edge" data structures such as grids or rasters, the need for certain types of complex topological modelling and analysis is clear. Current plane topology models such as the winged edge, widely used in computer aided design (CAD), are limited in the types of analysis that can be performed but useful because of their basis in the field of algebraic topology. This paper firstly reviews the neighborhood structure provided by current plane topological models. It then describes the derivation of a fundamental set of binary topological relationships between simple spatial primitives of like topological dimension in 3-space. It is intended that these relationships provide both a measure of modelling sufficiency and analytical ability in a spatial information system based on three dimensional neighborhoods. 1. Introduction Modelling and analysis of 3-dimensional spatial phenomena has become a critical need in many applications, particularly the earth sciences. One of the traditional approaches to the modelling problem is to subset the sampled data from the 3D phenomena into individual spatial objects based upon theme or convenience; each spatial object can then be decomposed into a set of abstract geometric primitives - points, lines, faces and volumes; and a set of spatial relationships describing how the object may be reconstructed from these primitives. Analysis of the spatial phenomena requires not only the spatial relationships between the primitives required to reconstruct individual spatial objects, but also those relationships describing how the individual spatial objects interact. Such an approach is one method by which spatial objects may be modelled and analyzed according to theme or view in a larger model of the real phenomena. 1 From April 11th, 1991, author's address will be: Centre for Spatial Information Studies, University of Tasmania, GPO Box 252C, Hobart, Tasmania, Australia, 7001. Internet email address: pigot@sol.surv.utas.oz.au 368