A Binary Tree Representation of Curve Hierarchical Structure in Depth

Map generalization has to take into account cartographic object properties in geometrical , semantic and topological aspects. As for line feature, simplification operators designed only from the viewpoint of angle, distance and vector characteristics are not true map generalization but geometrical compression, because it does not involve geographical properties contained in line. Due to the importance of curve bend characteristics in describing geographical meaning of line feature, the research of bend structure detection, representation and application in line abstracting becomes a focus in generalization field. This paper offers a method of bend definition rather than traditional one based on inflection points. The presented approach considers the Gestalt principles of symmetry, hierarchy and continuity in bend visual cognition. Constrained Delaunay triangulation model is used in the method and through triangle stripping trace the bend structure is recorded by the binary tree which describes the bend hierarchical levels. On the basis of bend binary tree structure, the paper divides the bends into basic bends and complex ones and defines a series of description parameter for both of them, including bend size, direction, average width, depth, and coverage region etc. These geo oriented descriptions apply triangulation skeleton, convex hull and other concepts in computation geometry. An application experiment of complex polygon simplification is conducted in this study according to small bend removal principles and the obtained effect is satisfactory.