found in [Chen et. al, 1995].
5.2. Integrated Reasoning of Spatial Relations
By using the models of spatial relations between sets presented
as above, we can integrally derive the compositions among
different kinds of spatial relations. It is possible to assess
whether it is a consistent query to ask for "all objects K, that are
farther then 100 meters between K, such that K, contains K,
and the distance between K,and K, isless than 100 meters",
we can integrally reason out the compositions between distance
and topological relations. by the following steps:
e since p(K,,K,) 2100 (m), K, 9 B(p, ,) covers K, ;
e since K, contains K,, K, @ B(p,, ,,) contains K, ;
e so that K @ B(p, 4) covers (or contains), K, and
PK, K,) S p(K,. K,) fsee Fig.97.
Ki
Vs i PIS My
\ 5. Kı@B(pi3) oh A
KER
Fig.9. Integrated reasoning the spatial relations of metric and topology.
6. CONCLUSIONS AND OUTLOOKS
As the natural extension of the general 9-intersection which is
used for formally deriving topological relations only, the
dynamic 9-intersection based on metric topology supplied a
general framework for studying different kinds of spatial
relations between sets. The presented integrated theory of
spatial relations between sets makes a new way for formally
deriving complex spatial relations among spatial objects with
uncertainties [Chen et. al., 1996], integrally reasoning metric,
order and topological spatial relations, and generation of the
related standards for transferring spatial relations [Mark et.
al., 1995]. Even though the presented approach is only focus on
the applications in GIS field, the related results for deriving
spatial relations between sets can be also used for many other
fields, such as CAD, computer vision, pattern recognition, robot
space searching and so on. However, only the theoretical
models and algorithms have be presented in this paper, a wide
field of practical application for data management and spatial
data analysis in 2-D and 3-D GIS environments has not been
touched. Therefore, the reported results must be verified and
extended in order to be used in different practical
environments.
Two main directions for further research shall be pointed here,
one is the applications of the presented theoretical models and
algorithms in 2-D and 3-D GIS environments for developing the
new tools of spatial query and analysis; another one is the
extensions of presented theories and models for formally
deriving complex spatial relations among spatial objects with
multiple representations.
104
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
ACKNOWLEDGMENTS
The authors wish especially to thank Prof. S. Murai and Mr.
H. Yamamoto for their considerable helps and supports of this
research project.
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