ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
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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
