e The relationship in applies if the former element is
completely contained in the latter one. This relation-
ship is transitiv and applies to all geometric elements.
e The relationship cross applies for the line/line,
line/area as well as for the line/body, area/body sit-
uation.
e The relationship overlap applies if the result of the
intersection is of the same dimension as the two par-
ticipating elements.
e The relationship disjoint expresses that no common
set exists.
In [Báhr, 1992] as well as in [Gapp, 1994] more predicates
are defined based on projective relations like above or behind.
Predicates of distance (e.g. near)or of order (e.g. between)
are also possible to implement.
The 2D predicates are realized mainly by the methods
surrounds??() and segpoint.near??(). Using coordinate
transforms and projections this methods can be used for the
computation of most of the 3D predicates.
Apart from predicates there are also object generating op-
erators (e.g. the results of intersections) and measurement
functions (e.g. the distance function). The distance will be
calculated at the level of and as a method of coordinates
(distance.to(another) resp. distance to line(a line)).
4.4 Representation in 3D
To display 3D objects considerable more complex algorithms
have to be used than those which are necessary to display
two-dimensional data. A 3D graphic program like Geomview
can be applied to minimize the costs of the implementation
and maximize the abilities of the conceive system. Changes
of viewpoints, rotation, scaling and selection of geoobjects
is thereby feasible without much effort. In the case of using
Geomview communication is possible in both direction.
Figure 5: Display of the landscape by Geomview
752
5 Summary
The three steps to a successful 3D implementation in an
existing 2.5D GIS are
e an additional data model for 3D data,
e methods to convert 3D data into 2D data to apply
2D operations and
e an external interactive 3D viewer for displaying 3D en-
tities.
Most GIS products will not allow extensions of that kind.
With Smallworld GIS we took advantage of the open object-
oriented interactive environment to try a possible implemen-
tation. The algorithm to transform all geometric objects has
already been implemented. Also methods have been imple-
mented to control Geomview and receive in turn information
about selected geometry.
Further work has to be done to implement the complete
data model to test its fitness and implement some more op-
erations.
References
Bähr, U. [1992], Untersuchungen zu räumlichen Abfrage-
sprachen, Diplomarbeit, TU München.
Egenhofer, M. J. and Franzosa, R. D. [1991], ‘Point-set topo-
logical spatial relations’, International Journal of Geo-
graphical Information Systems 5(2), 161-174.
Gapp, K.-P. [1994], A computational model of the basic
meanings of graded composite spatial relations in 3d
space, in Molenaar and de Hoop [1994], pp. 66-79.
Molenaar, M. and de Hoop, S., eds [1994], Advanced Geo-
graphic Data Modelling, number 40 in ‘Publications on
Geodesy’, Netherlands Geodetic Commision.
Rumbaugh, J., Plaha, M., Premerlani, W., Eddy, F. and
Lorensen, W. [1991], Objektorientiertes Modellieren
und Entwerfen, Prentice-Hall International and Verlag
Carl Hanser.
van Oosterom, P., Vertegaal, W., van Hekken, M. and Vi-
jlbrief, T. [1994], Integrated 3d modelling within a gis,
in Molenaar and de Hoop [1994], pp. 80-95.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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