Efficiently Generating Multiple Representations for Web Mapping

Line simplification is the most commonly used operation in map generalisation. In many commercial Geographic Information Systems (GIS), line simplification is performed by applying the classical Ramer-Douglas-Peucker (RDP) algorithm. However, such an algorithm has the drawback of not guaranteeing the preservation of topological consistency. This requires a posteriori checks to ensure that unwanted intersections introduced by the application of the algorithm get rectified. To overcome this problem, Saalfeld proposed a modification of the classical RDP algorithm based on the fact that, while generalising a polyline, conflicts can only occur with vertices of other polylines that lie within its convex hull. In this paper we propose an improvement to Saalfeld's algorithm to detect possible self-intersections of a simplified polyline more efficiently. This improves the performance especially when generalising very large datasets. Nevertheless, the processing time is still not acceptable for real-time web mapping. Therefore, we have integrated our algorithm into a web mapping system that pre-computes a sequence of topologically consistent map representations, stores them on the server, and transmits them progressively upon request. We present experimental results of the performance of the algorithm as well as results of the transmission system.

[1]  A. Saalfeld.  Topologically Consistent Line Simplification with the Douglas-Peucker Algorithm , 1999 .

[2]  J. Muller,et al.  The Removal of Spatial Conflicts in Line Generalization , 1990 .

[3]  M. Iri,et al.  Polygonal Approximations of a Curve — Formulations and Algorithms , 1988 .

[4]  Avraham A. Melkman,et al.  On-Line Construction of the Convex Hull of a Simple Polyline , 1987, Inf. Process. Lett..

[5]  Stefan Schirra,et al.  A new approach to subdivision simplification , 1995 .

[6]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[7]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[8]  Barbara P. Buttenfield,et al.  Transmitting Vector Geospatial Data across the Internet , 2002, GIScience.

[9]  Michela Bertolotto,et al.  Progressive vector transmission , 1999, GIS '99.

[10]  W. S. Chan,et al.  Approximation of Polygonal Curves with Minimum Number of Line Segments , 1992, ISAAC.

[11]  W. S. Chan,et al.  Approximation of Polygonal Curves with Minimum Number of Line Segments or Minimum error , 1996, Int. J. Comput. Geom. Appl..

[12]  Michela Bertolotto,et al.  Progressive Transmission of Vector Map Data over the World Wide Web , 2001, GeoInformatica.

[13]  Robert B McMaster,et al.  Automated Line Generalization , 1987 .

[14]  Michela Bertolotto,et al.  Exchanging Generalized Maps Across the Internet , 2004, KES.

[15]  Shin-Ting Wu,et al.  A non-self-intersection Douglas-Peucker algorithm , 2003, 16th Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI 2003).

[16]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[17]  J. Hershberger,et al.  Speeding Up the Douglas-Peucker Line-Simplification Algorithm , 1992 .

[18]  Mark R. Johnston,et al.  Problems Arising From A Simple GIS Generalisation Algorithm , 1999 .

[19]  Lakhmi C. Jain,et al.  Knowledge-Based Intelligent Information and Engineering Systems , 2004, Lecture Notes in Computer Science.