Synonyms
Quadtree; Q-tree; Octree; Data-structure, Spatial; Point-Quadtree; MX-Quadtree; PR-Quadtree; PM-Quadtree
Definition
A quadtree is a spatial data structure which has four branches attached to the branch point or node. The records exist in the leaf nodes of the tree. An octree is the same concept except the branches are in groups of eight. An octree can represent and image by subdividing the cubical volume. The quadtree tree is greatly used for two-dimensional space and the octree is used for three‐dimensional space.
Historical Background
The name quadtree has developed through time. It was once called a Q-tree and then later termed quadtree. It was adapted from the binary search tree in order to be used for two dimensions. The name octree simply comes from the prefix “oct” and the word tree. These data structures were needed in order to save space. These structures were first built as pointers, but have now evolved to use leaf nodes encoded by a locational code.
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Recommended Reading
Walid G.A., Ilyas, I.F.: A Framework for Supporting the Class of Space Partitioning Trees. TR01-002. Purdue University, West Lafayette, IN (2001)
Black, P.E. Quadtree. In: Dictionary of Algorithms and Data Structures. NIST Available via: http://www.nist.gov/dads/HTML/quadtree.html (2006)
Chandran, S., Gupta, A.K., Patgawkar, A.: A Fast Algorithm to Display Octrees. (2004) http://www.cse.iitb.ac.in/~sharat/papers/linearOctreee.pdf
Charlton, E.F.: The Octree. (1997)http://hpcc.engin.umich.edu/CFD/users/charlton/Thesis/html/node29.html. University of Michigan, Ann Arbor, MI, USA
Chern, H.-H., Fuchs, M., Hwang, H.-K.: Phase Changes in Random Point Quadtrees. National Taiwan Ocean University, National Chiao Tung University, and Institute of Statistical Science Academia Sinica, Taiwan. ACM Transact Algo 3(12):2 (2007)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press. Cambridge, MA (2001)
Finkel, R.A., Bentley, J.L.: Quad trees, A data structure for retrieval on composite keys. Acta Informatica (1974)
Frisken, S., Perry, R.: Simple and Efficient Traversal Methods for Quadtrees and Octrees. http://www.merl.com/reports/docs/TR2002-41.pdf
Heckbert, P.S., Garland, M.: Survey of Polygonal Surface Simplification Algorithms. In: SIGGRAPH 97 Course Notes, No. 25, ACM Press, New York (1997)
Hjaltason, G.R., Samet, H., Sussmann, Y.J.: Speeding up Bulk-Loading of Quadtrees. In: Proceedings of the 5th ACM international workshop on Advances in Geographic Information Systems, University of Maryland, Las Vegas, Nevada, USA (1997)
Meagher, D.J: Octree 3-D Geospatial Modeling Application: Artillery Shadows. http://www.octree.com/ArtilleryShadow/report.htm. Accessed 12 March 2007
Samet, H.: Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison-Wesley, Reading, MA (1990)
Savarese, D.F.: A Trio of Quadtrees. JAVAPro 7 November (2003)
Tayeb, J.: Design and Performance Evaluation of Indexing Methods for Dynamic Attributes in Mobile Database Management Systems. Master's thesis, Bilkent University, May 1997, Ankara, Turkey (1997)
Yoder, R.C.: Design Consideration for Implementing Complex Client/Server Applications: a Case Study of Octree-Based 3-D GIS. (1996)http://www.albany.edu/~sysrcy/dissertation/PR-11.TXT. Accessed 8 April 2006
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Sperber, M. (2008). Quadtree and Octree. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_1056
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