A Methodology Of Morphing Transformation Of Linear Features For Map Continuous Generalization

Continuous generalization is a new hot issue in the International Cartography Association (ICA), and also an important issue of both computer science and geographical information science. Continuous generalization aims to provide comfortable environment for map users, which allows the users to browse maps at any sacles and help to presever their focuses with an adaption to the change of the scale. Morphing is a kind of countinous transformation technology. This technology is so compatible for continuous generalization that it has been increasingly employed. For this purpose, this paper has investigated some problems of morphing transformation of linear features for map continuous generalization. It mainly includes following aspects:1. For a linear feature, one of its spatial characteristics is mainly represented by a set of bends. So a new morphing method for two linear features based on their bend structures is proposed. First, the bend structures of the linear features are identified by using a constrained Delaunay triangulation model, and represented by bend forest and binary bend structural trees. Second, corresponding independent bends are determined and further used to match their child bends based on hierarchical bend structure from higher level to lower level. In this case, the two linear features are partitioned into some pairs of correspondence (also called line segments). Third, the linear interpolation algorithm is employed to detect corresponding points for every pair of the corresponding line segments and the straight lines between corresponding points are utilized as moving trajectories for morphing.2. The extremal points are another important identifier for spatial characteristics of linear features, and then this paper proposes a new method of morphing for two linear features based on their BLG-tree (Binary Line Generalization Tree) structures. First, the structures of the linear features are identified by using Douglas-Peucker algorithm, and represented by the BLG-tree. Second, corresponding nodes are determined by matching the nodes of the BLG-trees from higher level to lower level. In this case, the two linear features can be partitioned into a set of corresponding line segments. Third, the linear interpolation algorithm is employed to detect corresponding points for every pair of the corresponding line segments and the straight lines between corresponding points are utilized as moving trajectories for morphing.3. River network is a typical spatial entity in the real world and its multi-scale transformation is a hot issue in the field of cartography and geographical information science. Therefore a multi-scale transformation approach for river network is proposed based on morphing technology. This approach involves two cases. One is to make transformation between two corresponding rivers, and the other is for some rivers represented only on the larger-scale map. As for the first case, shape interpolation is utilized for morphing, where the intersections between rivers and the structures of rivers themselves are considered. For the second case, an indicator is defined by the total length of a river and its tributaries, and is employed to measure the importance of the river. By using this indicator, some rivers of low importance, which are represented only on the larger-scale map, may be deleted in the process of multi-scale transformation.4. The issue on the change raw of lengths of interpolated linear features in morphing transformation has been investigated, which is very conducive to the determination of corresponding relationships between morphing degrees and map scales. To a pair of corresponding linear features, OptCor algorithm is utilized to detect corresponding points with the help of linear interpolation algorithm, and the straight lines between corresponding points are used as moving trajectories. On this basis, the method of regression analysis is employed to discover the change law, and it is verified that the lengths of interpolated linear features decrease in a quadratic curve way.