ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
concrete operation in building cluster generalization. How to use
them in a complete generalization process depends on workflow
control. Considering the fact that conflict in building cluster is
related to each other, we can not simply aggregate all the conflict
object which is connective. Aggregation of part of conflict object
and displacement may resolve the conflict between different part
groups. Especially when scale changes largely, the predefinition
of large conflict distance may lead to all building locating within
one street block are conflict. Obviously it is not proper to
combine all building into a big one. The whole control workflow of
building cluster generalization should be a progressive
procedure to remove conflict step by step.
If the distribution frequency of skeleton width covers a broad
range, and the width value is able to be obviously distinguished,
we can introduce MST method idea(Regnauld 1997) to control
the generalization procedure. It takes into account the distance
difference not only in quality between conflict and non-conflict
but also in quantity. The workflow is described briefly as follows.
Repeat the following steps until step i> finds no conflict:
i> Construct triangulation, compute GP and find conflict
skeleton, conflict building object.
ii> Sort the conflict skeleton on weighted width from short to
long.
iii> Scan conflict skeleton to check the related left and right
conflict OP. Two OPs can only remain current scanned
skeleton as conflict. Remove other conflict skeletons.
iv> Resolve remained conflicts using the above aggregation
method.
The above workflow guarantees each conflict removal happens
exactly between two buildings. Figure 11 illustrates some
procedures of building cluster generalization.
If the building distribution is random and the conflict s are few,
the above workflow can get proper generalized result. The
questions exist in next two aspects.
1> The early aggregated building will displace many times in
following processes and the position accuracy may be
damaged.
2> Distribution pattern can not be maintained.
The workflow improvement depends on further grouping the
conflict objects which have been identified by adjacent distance.
The mini distance difference is not able to distinguish building
group, requesting non-distance standard. The Gestalt nature in
building size, orientation, shape, distribution structure is an
important consideration fact.
Connecting center points within Voronoi diagram polygon gets
Fig. 12. The network of connective conflict
building object
dual geometric construction, Delaunay triangulation.
Correspondingly, based on building partitioning model,
connecting representative points of conflict building obtains
some connective networks, as shown in Figure 12. The further
works of this research in the future is to discover building
distribution pattern based on network analysis and combined
with other methods.
5. CONCLUSION
Based on Delaunay triangulation skeleton, this study constructs
a building partitioning model which is similar to Voronoi diagram.
The nature of equally separating space makes it a powerful tool
to analyze polygon distribution cluster. When applied in building
cluster generalization, it enables to solve conflict detection,
displacement offset and direction computation. The improved
distance computation between two buildings takes into account
the context environment and conforms to visual cognition. The
model and algorithm presented in the paper has been realized in
an interactive map generalization system.
Independent building simplification gets some achievements.
Building cluster generalization belongs to high level research
facing challenges. The representation and automatic recognition
of spatial distribution pattern is the first question to be resolved.
References
[1] Ai, T. , Guo, R. and Liu, Y. “ A Binary Tree Representation of
Bend Hierarchical Structure Based on Gestalt Principles”,
Proceedings of the 9 th International Symposium on Spatial
Data Handling, Beijing, pp2a43-56, 2000.
[2] Ai, T. and R. Z. Guo (2000): A Constrained Delaunay
Partitioning of Areal Objects to Support Map Generalization,
Journal of Wuhan Technical University of Surveying and
Mapping 25(1 ):35-41 ,(in Chinese).
[3] Bader, M. and R. Weibel (1997): Detecting and Resolving
Size and Proximity Conflicts in the Generalization of
Polygonal Maps, Proceedings of the 18 th ICC, Stockholm,
Sweden, Vol. 3: 1525-1532.
[4] Christensen, H. J. Albert (1999): Cartographic Line
Generalization with Waterlines and Medial-Axes,
Cartography and Geographic Information Science,
26(1 ):19-32.
[5] Federico Thomas (1998): Generating Street Center-Lines
From Vector City Maps , Cartography and Geographic
Information Systems, 25(4):221-230.
[6] Guo, R. Z. and T. H. Ai (2000): Simplification and Aggregation
of Building Polygons in Automatic Map Generalization,
Journal of Wuhan Technical University of Surveying and
Mapping, 25(1 ):25-30 (in Chinese).
[7] Heller, M.(1990): Triangulation Algorithm for Adaptive
Terrain Modeling, Proceedings of the 4 th International
Symposium on Spatial Data Handling, Zurich Swiss,
International Geographical Union, 163-174.
[8] Hernandez, D. and Clementini, E. (1995): Qualitative
Distance, Proceedings of COSIT’95,Semmering,
Austria:45-57.
[9] Jones, C. B., Bundy, G. L. and J. M. Ware (1995): Map
Generalization with a Triangulated Data Structure,
Cartography and GIS, 22(4): 317-331.
[10] Lee, D.(1999): New Cartographic Generalization Tools,
CD-Rom Proceedings of 19 ,h ICC, Ottawa , Section 8.
[11] Mackaness, W. A. and K. Beard (1993): Use of Graph
Theory to Support Map Generalization, Cartography and
Geographic Information Systems, 20(4):210-221.
[12] Mackaness, W. A. 1994. An Algorithm for Conflict