For many years, acquisition techniques and computational processes evolve
continually and the practical limitations of the use of 3D information
decrease. But in most of the cases and especially in urban contexts, the
evolution to real 3D geo-objects is rather slow. This could be explained by a
strong inhibitor factor, i.e. the inheritance of 2D way of thinking. The
primary reflex when upgrading a 2D model, for example the cadastral
model, may be to keep the 2D object’s definition and add some 3D
extensions. Even if the result is satisfactory, the approach is incomplete and
limitative. The opportunity of working with 3D data allows us to consider
the 3D world where many objects can significantly evolve. If an object has a
new definition strongly related to 3D (note that it can be therefore seen like
a new object), the use of a 3D model will be imperative by itself. To reach
this objective, adequate abstractions and manipulation tools should be used.
Among all, support of the 3D spatial analysis is most critical. In this order of
ideas, we will present a new 3D conceptual model (the Dimensional Model) for
describing real world and a new framework for representing spatial
relationships in R3.
Traditionally, the objects of interest in a GIS are considered spatial objects,
i.e. objects that have thematic and geometric characteristics. Consequently,
the word is about 3D GIS while the objects are geometrically represented in
three dimensions. Several extended studies have been done about the 3D
object of interest in urban environment. The common understanding is that
the most important 3D real objects in urban areas are buildings and terrain
represented as TIN (Grun and Dan 1997, Leberl and Gruber 1996, Tempfli
1998). Fuch 1996 presents a study on real objects of interest for 3D city
models. The investigations in five groups of objects (i.e. buildings,
vegetation, traffic network, public utilities and telecommunications) have
clearly shown the prevalent usage of (need for) buildings, traffic network
and vegetation. Razinger and Gleixner 1995 present a virtual model of a square
in Graz (created upon municipal request), containing buildings, traffic
network, lamp-posts and trees. Dahany 1997 suggests three groups of objects
to be considered: terrain, vegetation and built form. Clearly, most of the
authors address real objects with spatial extent. Operational data needed for
urban planning and especially cadastre, however, goes often far beyond the
real objects of interest discussed so far. For example, cadastral offices
maintain juridical boundaries and legal status of the real estate, i.e. items that
cannot be classified as 3D spatial objects. Zlatanova 2000 proposes objects as
people, companies, taxes, etc. to be included in the scope of objects
organised in a GIS. Four basic groups to distinguishing real objects are
introduced, i.e. juridical objects (e.g. individuals, institutions, companies),
topographic objects (e.g. buildings, streets, utilities), fictional objects (e.g.
administrative boundaries) and abstract objects (e.g. taxes, deeds, incomes).
Since all the objects have semantic characteristics, geometric characteristics
of real objects are the leading criterion of the grouping. There are objects
with either: 1) non-complete geometric characteristics (i.e. only location); 2)
complete geometric characteristics and existence in the real world; 3)
complete geometric characteristics and fictive existence; and 4) without
geometric characteristics.
According to this classification, the 3D topographic objects are basically the
3D spatial objects currently maintained (or intended for maintenance) in a
variety of information systems. The need of 3D fictional objects is usually
not that transparent. While it seems normal to evolve from a 2D
representation of building to a 3D representation (because this is the reality),
this is not the case for fictional object (municipality unit, statistical unit, or
other fictional phenomena).
The challenge of 3D GIS is to support analysis between all different types of
real objects. If 3D GIS incorporates only 3D topographic objects and no
3D fictional objects, some analysis would be simplified or even truncated.
Such simplification may also have the effect of a strong brake to the
evolution of 3D GIS. Therefore, in this paper, we will consider both
topographic and fictional objects as a part of our spatial relationship model.