Abstract
This paper describes an algorithm for generating a figure in a two-dimensional plane from a qualitative spatial representation of PLCA. In general, it is difficult to generate a figure from qualitative spatial representations, since they contain positional relationships but do not hold quantitative information such as position and size. Therefore, an algorithm is required to determine the coordinates of the objects while preserving the positional relationships. Moreover, it is more desirable that the resulting figure meets a user’s requirement. PLCA is a simple symbolic representation consisting of points, lines, circuits and areas. We have already proposed one algorithm for drawing, but the resulting figures are far from a “good” one. In that algorithm, we generate the graph corresponding to a given PLCA expression, decompose it into connected subgraphs, determine the coordinates in a unit circle for each subgraph independently, and finally determine the position and size of each subgraph by locating the circles in appropriate positions. This paper aims at generating a “good” figure for a PLCA expression. We use a genetic algorithm to determine the locations and the sizes of circles in the last step of the algorithm. We have succeeded in producing a figure in which objects are drawn as large as possible, with complex parts larger than others. This problem is considered to be a type of “circle packing,” and the method proposed here is applicable to the other problems in which locating objects in a non-convex polygon.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson, M., Meyer, N., Olivier, P. (eds.): Diagrammatic Representation and Reasoning. Springer, Berlin (2002)
Chartland, G., Lesniak, L.: Graphs & Digraphs, 3rd edn. Wadsworth & Brooks/Cole (1996)
Cohn, A.G.: A hierarchical representation of qualitative shape based on connection and convexity. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 311–326. Springer, Heidelberg (1995)
Cohn, A.G., Hazarika, S.M.: Qualitative spatial representation and reasoning: an overview. Fundamental Informaticae 46(1), 1–29 (2001)
Cohn, A.G., Varzi, A.: Mereotopological connection. Journal of Philosophical Logic 32, 357–390 (2003)
Egenhofer, M., Herring, J.: Categorizing binary topological relations between regions, lines and points in geographic databases. Technical Report. Department of Surveying Engineering, University of Maine (1990)
Egenhofer, M., Franzosa, R.: On the equivalence of topological relations. International Journal of Geographical Information Systems 9(2), 133–152 (1995)
Goldberg, D.E.: Genetic algorithms in search, - Optimization and machine learning. Kluwer Academic Publishers, Dordrecht (1989)
Grigni, M., Papadias, D., Papadimitriou, C.: Topological Inference. In: International Joint Conference on Artificial Intelligence, pp. 901–907 (1995)
Nedas, K., Egenhofer, M., Wilmsen, D.: Metric Details of Topological Line-Line Relations. International Journal of Geographical Information Science 21(1), 21–48 (2007)
Overmars, M., de Berg, M., van Kreveld, M., Schwarzkopf, O.: Computational Geometry. Springer, Berlin (1997)
Ochiai, N.: Introduction to Graph Theory: Application for Plane Graph. Nihon-Hyouron-sha (In Japanese) (2004)
Randell, D., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning (KR92), pp. 165–176. Morgan Kaufmann, San Francisco (1992)
Renz, J.: Qualitative Spatial Reasoning with Topological Information. In: Renz, J. (ed.) Qualitative Spatial Reasoning with Topological Information. LNCS (LNAI), vol. 2293, Springer, Heidelberg (2002)
Stock, O. (ed.): Spatial and Temporal Reasoning. Kluwer Academic Publishers, Dordrecht (1997)
Stephenson, K.: Circle packings in the approximation of conformal mappings. Bulletin of American Mathematics Society 23, 407–416 (1990)
Stephenson, K.: Introduction to circle packing - The theory of discrete analytic functions. Cambridge University Press, Cambridge (2005)
Sumitomo, T., Takahashi, K.: DLCS: Qualitative representation for spatial data. In: Twenty-first Annual Meeting of Japan Society for Software Science and Technology (In Japanese) (2004)
Sumitomo, T., Takahashi, K.: A qualitative treatment of spatial data. In: The 17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2005), pp. 539–548. IEEE Computer Society Press, Los Alamitos (2005)
Takahashi, K., Sumitomo, T.: A framework for qualitative spatial reasoning based on the connection patterns of regions. In: IJCAI-05 Workshop on Spatial and Temporal Reasoning, pp. 57–62 (2005)
Takahashi, K., Sumitomo, T., Takeuti, I.: On embedding a qualitative representation in a two-dimensional plane. In: IJCAI-07 Workshop on Spatial and Temporal Reasoning, pp. 101–109 (2007)
Williams, R.: Circle packings, plane tessellations, and networks. In: The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover, New York, pp. 34–47 (1979)
Wolter, F., Zakharyaschev, M.: Spatio-temporal representation and reasoning based on RCC-8. In: Proc. International Conference on Principles of Knowledge Representation and Reasoning (KR2000), pp. 3–14. Morgan Kaufmann, San Francisco (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kumokawa, S., Takahashi, K. (2007). Drawing a Figure in a Two-Dimensional Plane for a Qualitative Representation. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds) Spatial Information Theory. COSIT 2007. Lecture Notes in Computer Science, vol 4736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74788-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-74788-8_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74786-4
Online ISBN: 978-3-540-74788-8
eBook Packages: Computer ScienceComputer Science (R0)