DP1.6 - conclusion

From Line Geometry To Area Topology
by © P. Wade, M. Visvalingam and G.H. Kirby
CISRG Discussion Paper Series No 1, University of Hull, 48 pp

For the sake of posterity, please cite from the published version:
Kirby, G H, Visvalingam, M and Wade, P (1989) "The recognition and Representation of Polygons with Holes" Computer J, 32 (6), 554 - 562.

CONTENTS

Introduction
Background
Disassociative Area Model (DAM)
3.1 Geometry
3.2 Geography
3.3 Comparison of DAM with predecessors
Deriving the Topology
4.1 Extracting the Boundaries
4.2 Forming the Containment Hierarchy
An application of DAM
5.1 Background to the OS 1:625,000 Data
5.2 Extraction of the Geometric Topology
5.3 Identification of Area Objects
5 .4 Summary of the Project
Conclusion

REFERENCES
FIGURES It is best to open the figures in another browser window, so that you can read the text while studying the figures

6. CONCLUSION

This paper has made a number of contributions and raised several issues. These can be summarised as follows:

1) The paper presented a critical review of the major academic ideas on cartographic data structures to date. The functions of the unit line, unit boundary and unit of space were articulated in POLYVRT, HDS and GEOGRAF respectively. In ARC/INFO the geometric and geographic descriptions of area objects were divorced and connected through the unit of space.

2) We then described the Disassociative Area Model (DAM), which provides a synthesis of the above concepts. DAM is a conceptual description of the geometric components of polygonal area covers. The model identifies the essential functions of the unit line, unit boundary, unit of space and unit object of given data types. The unit of space (primitive region) continues to connect the geometric and geographic descriptions as in ARC/INFO. However, we believe that all descriptions can and should be made accessible by users through use of a single data model in ARC/INFO.

DAM's description of area topology utilises the concept of a tree of boundaries as proposed in HDS. This tree describes the containment relationships between the boundaries, and identifies the boundaries which define each primitive region. Boundaries in turn are composed of links (that is, node matched lines). However, unlike in HDS, GIRAS and ARC/INFO, the links refer to the boundaries on either side and not to the objects or primitive regions directly. The boundary thus becomes the connection between the unit line and unit of space.

3) The paper also outlined some data structures and algorithms for the automatic extraction of boundaries, the tree of boundaries, and thus the primitive regions, using only the geometric information. The algorithms and data structures could be adapted to suit specific requirements. For example, static and variable data sets would require slightly different representations.

4) DAM provides a convenient framework for the flexible input of geographic area information in a variety of formats and allows a partial verification of geometric and geographic components against each other. This was demonstrated by a case study in which we extracted a complete and coherent description, compatible with the DAM model, of hierarchically organised administrative areas from feature coded map details, that is, from fragments of information.

This was effected through ad hoc processes for integrating the geography with the geometry and for data validation. However, we believe that this should be (since it could be) effected through a general purpose GIS. In state‑ofthe‑art GIS, which tend to be based on the relational model, rule‑processing would be effected with relational operators. This may be an acceptable solution in the short term, but we believe that the relational model neither provides a natural user interface for rule‑processing, nor an ideal data model for cartographic phenomena.

We therefore believe that while existing GIS serve a useful role, their availability should not stifle the quest for fresh ideas.