ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
234 
aquisition, CAD is normally used for refining existing 3D data. 
The GIS method follows a totally different approach. Starting 
with huge quantities of existing 2D data, 3D objects are 
computed, using adaptive data structures: Two dimensional 
information (existing GIS data, digitized maps, orthophotos, 
etc.) combined with information about the altitude of the 
ground level where an object is placed (DTM) and joined with 
information about the height of an object (the third dimension) 
or more detailed data about their 3D shape (Pfund&Carosio 
1999). The advatage of this method is, that a 3D object always 
correspond with its 2D original, so all attributes of a 2D-GIS 
object can be used in the 3D GIS. But the problem remains, 
that three dimensional objects are usually generated newly 
every time they are used. While this is quite handy for 'simple' 
objects which are stored two-dimensionally and a three- 
dimensional Symbol is applied at request, it limits the 
possibilities for handling more complex objects (e g. buildings) 
with individual shapes. 
2.2 Data Analysis and Output 
3D vizualisation is a task, most systems have solved the one 
or other way. One can observe different solutions, ranging 
from rather static 3D views to VRML applications and to 
spcialized frontends like ESRI’s Spatial Analyst. 
On the other hand is all systems widely common, that they do 
support only few analysis functionality if any at all. You allways 
can perform some visual analysis on a 3D output like the 
estimation of the impact of a new building on the environment, 
but others are often lacking, e g. distance functions in the third 
dimension, overlay operations, mathematical operations like 
buffering, volume and surface area calculations or other 
specific capabilities (Giger&Loidold 2001). 
Concluding, one can say that today most applications and data 
structures for 3D geodata are optimised for visualisation 
Normally they omit GIS relevant information not needed for a 
visualisation as for example topology or thematic attributes 
other than texture or symbolisation. Mainly in order to get a 
better performance but also to limit the complexity of systems. 
As consequence of these simplifications the funcionality 
available is usually limited to pure visualisation and data 
aquisition while possibilities for data management and analysis 
are missing to a large extent. If however the entire spectrum of 
Constructive Solid Geometry 
Fig. 2: Basic geometric modelling concepts for 3D-GIS: Spatial 
Enumeration, CSG and B-Rep. 
functionality we know from 2D GIS (acquisition, administration, 
analysis and presentation) is to be available in a 3D GIS, we 
need an adequate geometric data structure. 
3 MODELLING CONCEPTS FOR 3D OBJECTS 
The geometrical data model is a very significant component of 
a 3D-GIS. While the basic modeling techniques for 
representing 3D-objects in computers are widely known and 
used for quite a long time in CAD applications, they were 
implemented only most recently and partially in GIS. However 
in order to take into account the special conditions of GIS the 
data models must be adapted. 
In order to be able to process real world objects in computers, 
they must be mapped into a data model. This mapping can 
only be achieved, like with 2D-GIS, by an abstraction of the 
real objects. This internal computer representation establishs 
in terms of a suitable memory structure and together with the 
appropriate algorithms the base for the applications. The goal 
of geometrical modelling is to describe and manage solid 
objects with high, respectively with to the requirements 
adapted quality. 
For the quality of the representation the following five criteria 
can be intended (Requita 1980, Streilein 1999): 
• Definition range 
• Completeness 
• Unambiguousness 
• Compactness 
• Efficiency 
Quantity of the objects, which 
can be represented 
Geometrical quality (accuracy, 
level of detail). 
An object is unique, if there 
exists to each object exactly one 
representation and to each 
representation exactly one 
object. 
Storage space needed. 
Computing time for creation, 
analyse and processing. 
These partially competing requests often require compromises 
during implementations, like the optimisation of storage 
volume and computing time. 
Due to different computer-internal representations and 
applicatoin ranges 3D computer models three classes can 
be distinguished: Wireframes, surface models and solid 
models. Because wireframes and surface models are unapt 
for modelling bodies (FTund.Carosio 1999, Pfund 1999) this 
paper only presents three different types of solid models all 
used in GIS applications. 
3.1 Solid Models 
The goal of solid models is, contrary to other 3D-models 
which often are only sutiable for special applications, to 
create generally applicable models. Because only „complete" 
representations of physical bodies are accepted, systems 
which use solid models are (theoretically) able to answer 
geometrical questions algorithmically whitout interactive 
intervention by a user. „Complete" means that it should not 
be possible to define bodies with missing surfaces. 
3.1.1 Spatial Enumeration 
With cell models solids are approximated by voxels of 
uniform size, the three-dimensional analogue to the pixel. 
The voxels are arranged in a regular spatial lattice and are 
computer-intemally represented by the coordinates of the 
center of the cell. An object is therefore an arrangement of 
neighbouring cells in the space. The resolution of the model 
is specified by the cell size. 
The representation of 3D objects with spatial enumeration is 
suitable for the calculation of volumes and other boolean 
operations (additions, subtractions) as well as for