An Efficient and Topologically Correct Map Generalization Heuristic

Mauricio G. Gruppi, Salles V. G. de Magalhães, Marcus V. A. Andrade, W. Randolph Franklin, Wenli Li


We present TopoVW, an efficient heuristic for map simplification that deals with a variation of the generalization problem where the idea is to simplify the polylines of a map without changing the topological relationships between these polylines or between the lines and control points. This process is important for maintaining clarity of cartographic data, avoiding situations such as high density of map features, inappropriate intersections. In practice, high density of features may be represented by cities condensed into a small space on the map, inappropriate intersections may produce intersections between roads, rivers, and buildings. TopoVW is a strategy based on the Visvalingam-Whyatt algorithm to create simplified geometries with shapes similar to the original map, preserving topological consistency between features in the output. It uses a point ranking strategy, in which line points are ranked by their effective area, a metric that determines the impact a point will cause to the geometry if removed from the line. Points with inferior effective area are eliminated from the original line. The method was able to process a map with 4 million line points and 10 million control points in less than 2 minutes on a Intel Core 2 Duo processor.


  1. ACM SIGSPATIAL Cup (2014). GIS Cup sample data. xzhang22/GISCUP2014/ (accessed on 12/01/2014).
  2. Da Silva, A. C. and Wu, S.-T. (2005). Preserving coincidence and incidence topologies in saalfeld's polyline simplification algorithm. In Proceedings of Simposio Brasileiro de Geoinformatica (GeoInfo), pages 107- 121. INPE.
  3. Dettori, G. and Falcidieno, B. (1982). An algorithm for selecting main points on a line. Computers & Geosciences, 8(1):3-10.
  4. 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.
  5. Estkowski, R. and Mitchell, J. S. (2001). Simplifying a polygonal subdivision while keeping it simple. In Proceedings of the seventeenth annual symposium on Computational geometry, pages 40-49. ACM.
  6. Franklin, W. R., Narayanaswami, C., Kankanhalli, M., Sun, D., Zhou, M.-C., and Wu, P. Y. (1989). Uniform grids: A technique for intersection detection on serial and parallel machines. In Proceedings of Auto-Carto, volume 9, pages 100-109.
  7. IBGE: Instituto Brasileiro de Geografia e Estatistica (2014). Malhas digitais dos municipios Brasileiros. digitais/municipio 2007/ (accessed on 12/01/2014).
  8. Joa˜o, E. (1998). Causes and Consequences of map generalization. CRC Press.
  9. Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598):671-680.
  10. Li, L., Wang, Q., Zhang, X., and Wang, H. (2013). An algorithm for fast topological consistent simplification of face features. Journal of Computational Information Systems, 9(2):791-803.
  11. Mackaness, W. A., Ruas, A., and Sarjakoski, L. T. (2011). Generalisation of geographic information: cartographic modelling and applications. Elsevier.
  12. Magalha˜es, S. V. G., Franklin, W. R., Li, W., and Andrade, M. V. A. (2014). Fast map generalization heuristic with a uniform grid. In ACM SIGSPATIAL.
  13. Ramer, U. (1972). An iterative procedure for the polygonal approximation of plane curves. Computer Graphics and Image Processing, 1(3):244-256.
  14. Robergé, J. (1985). A data reduction algorithm for planar curves. Computer Vision, Graphics, and Image Processing, 29(2):168-195.
  15. Ruas, A. and Lagrange, J.-P. (1995). Data knowledge and modelling for generalization. MULLER, JC, LAGRANGE, JP, WEIBEL, R. GIS and generalization: metodology and practice. GISDATA I, serie editors, pages 73-90.
  16. Saalfeld, A. (1999). Topologically consistent line simplification with the douglas-peucker algorithm. Cartography and Geographic Information Science, 26(1):7-18.
  17. Shea, K. and McMaster, R. B. (1989). Cartographic generalization in a digital environment: When and how to generalize. In Proceedings of AutoCarto.
  18. United States Census (2014). US counties Shapefiles. (accessed on 12/01/2014).
  19. Visvalingam, M. and Whyatt, J. (1993). Line generalisation by repeated elimination of points. The Cartographic Journal, 30(1):46-51.
  20. Ware, J. M., Jones, C. B., and Thomas, N. (2003). Automated map generalization with multiple operators: a simulated annealing approach. International Journal of Geographical Information Science, 17:743-769.

Paper Citation

in Harvard Style

G. Gruppi M., V. G. de Magalhães S., V. A. Andrade M., Randolph Franklin W. and Li W. (2015). An Efficient and Topologically Correct Map Generalization Heuristic . In Proceedings of the 17th International Conference on Enterprise Information Systems - Volume 1: ICEIS, ISBN 978-989-758-096-3, pages 516-525. DOI: 10.5220/0005398105160525

in Bibtex Style

author={Mauricio G. Gruppi and Salles V. G. de Magalhães and Marcus V. A. Andrade and W. Randolph Franklin and Wenli Li},
title={An Efficient and Topologically Correct Map Generalization Heuristic},
booktitle={Proceedings of the 17th International Conference on Enterprise Information Systems - Volume 1: ICEIS,},

in EndNote Style

JO - Proceedings of the 17th International Conference on Enterprise Information Systems - Volume 1: ICEIS,
TI - An Efficient and Topologically Correct Map Generalization Heuristic
SN - 978-989-758-096-3
AU - G. Gruppi M.
AU - V. G. de Magalhães S.
AU - V. A. Andrade M.
AU - Randolph Franklin W.
AU - Li W.
PY - 2015
SP - 516
EP - 525
DO - 10.5220/0005398105160525