1 research outputs found
Applications of continuous functions in topological CAD data
Most CAD or other spatial data models, in particular boundary representation
models, are called "topological" and represent spatial data by a structured
collection of "topological primitives" like edges, vertices, faces, and
volumes. These then represent spatial objects in geo-information- (GIS) or CAD
systems or in building information models (BIM). Volume objects may then either
be represented by their 2D boundary or by a dedicated 3D-element, the "solid".
The latter may share common boundary elements with other solids, just as
2D-polygon topologies in GIS share common boundary edges. Despite the frequent
reference to "topology" in publications on spatial modelling the formal link
between mathematical topology and these "topological" models is hardly
described in the literature. Such link, for example, cannot be established by
the often cited nine-intersections model which is too elementary for that
purpose. Mathematically, the link between spatial data and the modelled "real
world" entities is established by a chain of "continuous functions" - a very
important topological notion, yet often overlooked by spatial data modellers.
This article investigates how spatial data can actually be considered
topological spaces, how continuous functions between them are defined, and how
CAD systems can make use of them. Having found examples of applications of
continuity in CAD data models it turns out that of continuity has much
practical relevance for CAD systems