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HandWiki. Fat Object. Encyclopedia. Available online: https://encyclopedia.pub/entry/36879 (accessed on 02 October 2026).
HandWiki. Fat Object. Encyclopedia. Available at: https://encyclopedia.pub/entry/36879. Accessed October 02, 2026.
HandWiki. "Fat Object" Encyclopedia, https://encyclopedia.pub/entry/36879 (accessed October 02, 2026).
HandWiki. (2022, November 28). Fat Object. In Encyclopedia. https://encyclopedia.pub/entry/36879
HandWiki. "Fat Object." Encyclopedia. Web. 28 November, 2022.
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In geometry, a fat object is an object in two or more dimensions, whose lengths in the different dimensions are similar. For example, a square is fat because its length and width are identical. A 2-by-1 rectangle is thinner than a square, but it is fat relative to a 10-by-1 rectangle. Similarly, a circle is fatter than a 1-by-10 ellipse and an equilateral triangle is fatter than a very obtuse triangle. Fat objects are especially important in computational geometry. Many algorithms in computational geometry can perform much better if their input consists of only fat objects; see the applications section below.
computational geometry
ellipse
equilateral
References
- Katz, M. J. (1997). "3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects". Computational Geometry 8 (6): 299–316. doi:10.1016/s0925-7721(96)00027-2. , Agarwal, P. K.; Katz, M. J.; Sharir, M. (1995). "Computing depth orders for fat objects and related problems". Computational Geometry 5 (4): 187. doi:10.1016/0925-7721(95)00005-8. https://dx.doi.org/10.1016%2Fs0925-7721%2896%2900027-2
- Efrat, A.; Katz, M. J.; Nielsen, F.; Sharir, M. (2000). "Dynamic data structures for fat objects and their applications". Computational Geometry 15 (4): 215. doi:10.1016/s0925-7721(99)00059-0. https://dx.doi.org/10.1016%2Fs0925-7721%2899%2900059-0
- Van Der Stappen, A. F.; Halperin, D.; Overmars, M. H. (1993). "The complexity of the free space for a robot moving amidst fat obstacles". Computational Geometry 3 (6): 353. doi:10.1016/0925-7721(93)90007-s. https://dx.doi.org/10.1016%2F0925-7721%2893%2990007-s
- Berg, M.; Groot, M.; Overmars, M. (1994). "New results on binary space partitions in the plane (extended abstract)". Algorithm Theory — SWAT '94. Lecture Notes in Computer Science. 824. pp. 61. doi:10.1007/3-540-58218-5_6. ISBN 978-3-540-58218-2. , Van Der Stappen, A. F.; Overmars, M. H. (1994). "Motion planning amidst fat obstacles (extended abstract)". Proceedings of the tenth annual symposium on Computational geometry - SCG '94. pp. 31. doi:10.1145/177424.177453. ISBN 978-0897916486. , Overmars, M. H. (1992). "Point location in fat subdivisions". Information Processing Letters 44 (5): 261–265. doi:10.1016/0020-0190(92)90211-d. , Overmars, M. H.; Van Der Stappen, F. A. (1996). "Range Searching and Point Location among Fat Objects". Journal of Algorithms 21 (3): 629. doi:10.1006/jagm.1996.0063. https://dx.doi.org/10.1007%2F3-540-58218-5_6
- "How fat is a triangle?". https://math.stackexchange.com/q/915187. Retrieved 28 September 2014.
- Weisstein, Eric W. "Inradius". http://mathworld.wolfram.com/Inradius.html. Retrieved 28 September 2014.
- See graph at: https://www.desmos.com/calculator/fhfqju02sn
- Mark de Berg; Onak, Krzysztof; Sidiropoulos, Anastasios (2010). "Fat Polygonal Partitions with Applications to Visualization and Embeddings". Journal of Computational Geometry Vol 4. doi:10.20382/jocg.v4i1a9. https://dx.doi.org/10.20382%2Fjocg.v4i1a9
- De Berg, Mark; Speckmann, Bettina; Van Der Weele, Vincent (2014). "Treemaps with bounded aspect ratio". Computational Geometry 47 (6): 683. doi:10.1016/j.comgeo.2013.12.008. . Conference version: "Convex Treemaps with Bounded Aspect Ratio". EuroCG. 2011. http://alexandria.tue.nl/openaccess/Metis253577.pdf.
- Segal-Halevi, Erel; Nitzan, Shmuel; Hassidim, Avinatan; Aumann, Yonatan (2017). "Fair and square: Cake-cutting in two dimensions". Journal of Mathematical Economics 70: 1–28. doi:10.1016/j.jmateco.2017.01.007. https://dx.doi.org/10.1016%2Fj.jmateco.2017.01.007
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