Abstract
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.
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References
Bader M. and Weibel R. (1997) Detecting and resolving size and proximity conflicts in the generalization of polygonal maps. pages 1525–1532.
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.
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.
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.
De Berg M., Van Kreveld M., and Schirra S. (1998) Topologically Correct Subdivision Simplification Using the Bandwidth Criterion. Cartography and Geographic Information Science, 25:243–257.
Douglas D. H. and Peucker T. K. (1973) Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2):112–122.
Dyken C., Dæhlen M., and Sevaldrud T. (2009) Simultaneous curve simplification. Journal of Geographical Systems, 11(3):273–289.
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.
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.
Kulik L., Duckham M., and Egenhofer M. (2005) Ontology-driven map generalization. Journal of Visual Languages & Computing, 16(3):245–267.
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.
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.
Ohori K. A. (2010) Validation and automatic repair of planar partitions using a constrained triangulation. Master’s thesis, Delft University of Technology.
Plümer L. and Gröger G. (1997) Achieving integrity in geographic information systems—maps and nested maps. Geoinformatica, 1(4):345–367.
Ramer U. (1972) An iterative procedure for the polygonal approximation of plane curves. Computer Graphics and Image Processing, 1(3):244–256.
Saalfeld A. (1999) Topologically Consistent Line Simplification with the Douglas- Peucker Algorithm. Cartography and Geographic Information Science, 26:7–18.
Van Oosterom P. (1990) Reactive Data Structures for Geographic Information Systems. Ph.D. thesis, Leiden University.
Van Oosterom P. (2005) Variable-scale Topological Data Structures Suitable for Progressive Data Transfer: The GAP-face Tree and GAP-edge Forest. Cartography and Geographic Information Science, 32:331–346.
Visvalingam M. and Whyatt J. D. (1993) Line generalisation by repeated elimination of points. The Cartographic Journal, 30(1):46–51.
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Meijers, M. (2011). Simultaneous & topologically-safe line simplification for a variable-scale planar partition. In: Geertman, S., Reinhardt, W., Toppen, F. (eds) Advancing Geoinformation Science for a Changing World. Lecture Notes in Geoinformation and Cartography(), vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19789-5_17
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DOI: https://doi.org/10.1007/978-3-642-19789-5_17
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