Years and Authors of Summarized Original Work
2002; Hjaltason, Samet
2006; Agarwal, Arge, Danner
2010; de Berg, Haverkort, Thite, Toma
2013; McGranaghan, Haverkort, Toma
Problem Definition
The quadtree describes a class of data structures for geometric objects. A quadtree partitions space hierarchically using a stopping rule that decides when a region is small enough so that it does not need to be subdivided further. If the space is d dimensional, a quadtree recursively divides a d-dimensional hypercube containing the input data into 2d hypercubes until each region satisfies the given stopping rule. In 2D, the hypercubes are squares. Three-dimensional quadtrees are also known as octrees. Quadtrees have been used for many types of data, such as points, line segments, polygons, rectangles, curves, and images, and for many types of applications. For a detailed presentation, we refer to the book by Samet [10]. While their worst-case behavior is good only in some simple cases, quadtrees...
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Agarwal PK, Arge L, Danner A (2006) From point cloud to grid DEM: a scalable approach. In: Proceedings of the 12th symposium on spatial data handling, Vienna, pp 771–788
de Berg M, Haverkort H, Thite S, Toma L (2010) Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions. Comput Geom 43(5):493–513
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Haverkort, H., Toma, L. (2016). Quadtrees and Morton Indexing. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_585
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DOI: https://doi.org/10.1007/978-1-4939-2864-4_585
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