Sorting in space

Abstract

The representation of spatial data is important in game programming, computer graphics, visualization, solid modeling, computer vision and geographic information systems (GIS). They are rooted in the intersection of computer vision and graphics. Recently, there has been much interest in hierarchical representations such as quadtrees, octrees, and pyramids which are based on image hierarchies, as well methods that use bounding boxes which are based on object hierarchies. Their advantage is that they provide a way to index into space. In fact, they are little more than multidimensional sorts. They save space as well as time and also facilitate operations such as search. In addition, we introduce methods for dealing with recognizing textual specifications of spatial data such as locations in news articles.This course provides a brief overview of hierarchical spatial data structures and related algorithms that make use of them. We describe hierarchical representations of points, lines, collections of small rectangles, regions, surfaces, and volumes. For region data, we point out the dimension-reduction property of the region quadtree and octree, as how to navigate between nodes in the same tree, thereby leading to the popularity of these representations in ray tracing applications. We also demonstrate how to use these representations for both raster and vector data. We also In the case of nonregion data, we show how these data structures can be used to find nearest neighbors which is critical when using machine learning techniques. We also show how to do it in an incremental fashion so that the number of objects need not be known in advance. In addition, the SAND spatial browser based on the SAND spatial database system, the VASCO JAVA applet illustrating these methods (www.cs.umd.edu/ hjs/quadtree/index.html), and the NewsStand system (newsstand.umiacs.umd.edu) will be demonstrated.