Most CAD or other spatial data models, in particular boundary representationmodels, are called "topological" and represent spatial data by a structuredcollection of "topological primitives" like edges, vertices, faces, andvolumes. These then represent spatial objects in geo-information- (GIS) or CADsystems or in building information models (BIM). Volume objects may then eitherbe represented by their 2D boundary or by a dedicated 3D-element, the "solid".The latter may share common boundary elements with other solids, just as2D-polygon topologies in GIS share common boundary edges. Despite the frequentreference to "topology" in publications on spatial modelling the formal linkbetween mathematical topology and these "topological" models is hardlydescribed in the literature. Such link, for example, cannot be established bythe often cited nine-intersections model which is too elementary for thatpurpose. Mathematically, the link between spatial data and the modelled "realworld" entities is established by a chain of "continuous functions" - a veryimportant topological notion, yet often overlooked by spatial data modellers.This article investigates how spatial data can actually be consideredtopological spaces, how continuous functions between them are defined, and howCAD systems can make use of them. Having found examples of applications ofcontinuity in CAD data models it turns out that of continuity has muchpractical relevance for CAD systems.
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