Simultaneous & topologically-safe line simplification for a variable-scale planar partition
We employ a batch generalization process for obtaining a variable- scale planar partition. We describe an algorithm to simplify the boundary lines after a map generalization operation (either a merge or a split operation) has been applied on a polygonal area and its neighbours. The simplification is performed simultaneously on the resulting boundaries of the new polygonal areas that replace the areas that were processed. As the simplification strategy has to keep the planar partition valid, we define what we consider to be a valid planar partition (among other requirements, no zero-sized areas and no unwanted intersections in the boundary polylines). Furthermore, we analyse the effects of the line simplification for the content of the data structures in which the planar partition is stored.
KeywordsLine Simplification Planar Partition Boundary Cycle Split Operation Polygonal Area
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- Bader M. and Weibel R. (1997) Detecting and resolving size and proximity conflicts in the generalization of polygonal maps. pages 1525–1532.Google Scholar
- Barkowsky T., Latecki L. J., and Richter K. F. (2000) Schematizing Maps: Simplification of Geographic Shape by Discrete Curve Evolution. In Spatial Cognition II, volume 1849 of Lecture Notes in Computer Science, pages 41– 53. Springer Berlin / Heidelberg.Google Scholar
- Bentley J. L. (1990) K-d trees for semidynamic point sets. In SCG ’90: Proceedings of the sixth annual symposium on Computational geometry, pages 187– 197. ACM, New York, NY, USA.Google Scholar
- Da Silva A. C. G. and Wu S. T. (2006) A Robust Strategy for Handling Linear Features in Topologically Consistent Polyline Simplification. In AMV Mon Geoinformatics, 19–22 November, Campos do Jordão, São Paulo, Brazil, pages 19– 34.Google Scholar
- Gröger G. and Plümer L. (1997) Provably correct and complete transaction rules for GIS. In GIS ’97: Proceedings of the 5th ACM international workshop on Advances in geographic information systems, pages 40–43. ACM, New York, NY, USA.Google Scholar
- Guibas L. J. and Sedgewick R. (1978) A dichromatic framework for balanced trees. In 19th Annual Symposium on Foundations of Computer Science, 1978, pages 8–21.Google Scholar
- Ledoux H. and Meijers M. (2010) Validation of Planar Partitions Using Constrained Triangulations. In Proceedings Joint International Conference on Theory, Data Handling and Modelling in GeoSpatial Information Science, pages 51–55. Hong Kong.Google Scholar
- Meijers M., Van Oosterom P., and Quak W. (2009) A Storage and Transfer Efficient Data Structure for Variable Scale Vector Data. In Advances in GIScience, Lecture Notes in Geoinformation and Cartography, pages 345–367. Springer Berlin Heidelberg.Google Scholar
- Ohori K. A. (2010) Validation and automatic repair of planar partitions using a constrained triangulation. Master’s thesis, Delft University of Technology.Google Scholar
- Van Oosterom P. (1990) Reactive Data Structures for Geographic Information Systems. Ph.D. thesis, Leiden University.Google Scholar