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AN INDIRECT GENERALIZATION OF CONTOUR LINES BASED ON DEM GENERALIZATION USING THE 3 D DOUGLAS-PEUCKER ALGORITHM

In order to simplify the generalization of contour lines during the compilation of maps at smaller scales, an indirect method is put forward based on the generalization of the corresponding DEM first using the 3 dimensional Douglas-Peucker (3D D-P) algorithm before the final contour lines are derived. Preliminary experiments show that the Douglas-Peucker algorithm can be expanded to 3D and it is suitable for the global generalization of DEMs. Furthermore, the derived contour lines from the generalized DEMs can maintain the macro relief form while depress the micro geo-morphological vibration. It is concluded that the indirect generalization of contour lines based on the DEM generalization using 3D D-P algorithm is a promising way according to its speed and quality in the generalization. INTRODUCTION OF THE DEVELOPMENT HISTORY FOR THE AUTOMATED GENERALIZATION OF CONTOUR LINES To describe the relief forms on the earth’s surface, contour lines have been used widely no matter for manual or computer assisted cartography (Hake and Grünreich, 1994). It is suitable for hydrologic analysis, simulation of relief forms, and cartographic display such as contour lines or layer tinting for the map readers and can even be a data basis for establishing a Digital Elevation Model (DEM) (Tang et al., 2005). Because of their measurability of the height of any point on a map, the contour lines are still a necessary part of topographic maps. However, the methods of generalization of contour lines during the compilation of maps at smaller scales are usually quite complicated because while being simplified with topological coherence (Zhang et al., 2007), the generalized contour lines should reflect the main characteristics of the relief form. At least, the solution of this problem cannot rely on the simplification of the individual contour lines’ figures although some good algorithms for simplifying the figures of the individual curves were suggested in 1970’s. Since the end of 1970’s, many scientists have suggested or designed the methods of automated group-wise generalization of the contour lines (Hentschel, 1979; Wu, 1982). Until now, it seems to be a necessary and important step to search for the geo-morphological structural lines first which are implicitly described by the contour data. They act as the framework for organizing the bends of the contour lines. Only after these structural lines have been properly generalized, can one decide which valleys or ridges should be selected, merged and others deleted through maintaining or changing the local figures of the corresponding contour lines harmonically in groups (Fei, 1993; Wu, 1995; Ai, 2007). Obviously, the process of this kind of generalization of contour lines is rather complicated because it is a hard task to find out all the implicit geo-morphological structural lines which are hidden behind the local figures of the adjacent and nearby contour lines. Besides, one must organize nearly all the bends on the contour lines into various geo-morphological structural lines before the generalization of these structural lines is implemented. Finally, it is not an easy job to decide what the simplified figures of the contour lines in groups should be even if, say, a valley is to be deleted, since instead of the old bends, the proper new loci of the contour lines have to be decided by the geographical context of the vicinity, cartographically speaking. Hence, it is a task for digital cartographers and GIS developers to look for a new method of generalization of contour lines for faster and better generalization results. DEMS AND THE RELATIONSHIP BETWEEN CONTOUR LINES AND DEMS A digital elevation model (DEM) can be seen as a kind of data with a certain format to describe the relief form of the earth’s surface. The data about three dimensions of every point are necessary. It is widely used for extracting various relief parameters such as elevation, slope, slope aspect, roughness and so on, and can be used for sight analysis, generation of drainage basin structure, calculation of earthwork amount, automated hill shading map-making, etc (Zhou and Liu, 2006). It is also possible to expand the concept of DEM to various attribute amounts relevant to the earth’s surface (Li and Zhu, 2000). Therefore, DEM has been widely used in a lot of fields. The data representation of DEM has many forms, among which are 3D randomly distributed point sets, regular square grids (RSG), arranged points on parallel profiles, points along contour lines, triangular irregular network (TIN), etc. (Hake et al., 2002). From the above discussion, points along the contour lines can be regarded just as one of the DEM types. If a generic format of DEM is to be found to include all kinds of the above mentioned DEMs, that is none other than the 3D randomly distributed discrete points with or without constraints. All other types of DEMs can be seen as its special cases. Therefore, if the DEM with the format 3D randomly distributed discrete points can be generalized correctly, why can’t the other types of DEMs, including the points along the contour lines? If contour lines are derived from the generalized DEM, could they reflect the