On multi-scale display of geometric objects

摘要

An important requirement in Geographic Information Systems (GISs) is the ability to display numerous geometric objects swiftly onto the display window. As the screen size is fixed, the scale of a map displayed changes as the user zooms in and out of the map. Spatial indexes like R-tree variants that are particularly efficient for range queries are not adequate to generate large maps that may be displayed at different scales. We propose a generalization for the family of R-trees, called the Multi-scale R-tree, that allows efficient retrieval of geometric objects at different levels of detail. The remedy offered here consists of two generalization techniques is cartography: selection and simplification. Selection means some objects that are relatively unimportant to the user at the current scale will not be retrieved. Simplification means that, given a scale, the display of objects is shown with sufficient but not with unnecessary detail. These two together reduce the time required to generate a map on a screen. A major obstacle to the effectiveness of a Multi-scale R-tree is the proper decomposition of geometric objects required by the simplification technique. To investigate the problem, a Multi-scale Hilbert R-tree is designed and implemented. Extensive experiments are then performed on real-life data and a general and simple design heuristic is found to solve the decomposition problem. We show that, with the proposed design heuristic, the Multi-scale R-tree is a desirable spatial index for both querying and display purposes.