Abstract
Applications in cartography, computer graphics and computer aided engineering require the representation and manipulation of planar subdivisions. Topology-oriented approaches represent the relations existing between the vertices, edges and faces of a planar subdivision. We extend this standard approach by decomposing the faces into trapezoidal views. By defining a neighborhood relation among the views we obtain the view graph which forms the basis of the quad view data structure — a new data structure for representing planar subdivisions. We present some basic operations on this data structure, and we show how it can be used to traverse a planar subdivision. Furthermore we sketch an algorithm for overlaying planar subdivisions represented by the quad view data structure. This algorithm is optimal for simply connected planar subdivisions: its time and storage requirements are linear in the size of the output subdivision. Finally we apply this overlay algorithm to implement locational vector-based map overlay operations.
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© 1995 Springer-Verlag Berlin Heidelberg
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Finke, U., Hinrichs, K.H. (1995). The quad view data structure — a representation for planar subdivisions. In: Egenhofer, M.J., Herring, J.R. (eds) Advances in Spatial Databases. SSD 1995. Lecture Notes in Computer Science, vol 951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60159-7_3
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DOI: https://doi.org/10.1007/3-540-60159-7_3
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