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Works Cited

Aurenhammer, Franz, and Rolf Klein. Voronoi Diagrams. Fernuniversität, 1996. 

General background on history and explanation of the largest empty circle problem.

Austin, David. “Voronoi Diagrams and a Day at the Beach.” American Mathematical

Society, 

Aug. 2006, www.ams.org/publicoutreach/feature-column/fcarc-voronoi. 

Information on the Voronoi diagram created for the cholera outbreak and on creating voronoi diagrams with perpendicular bisectors. 

Dobrin, Adam. A Review of Properties and Variation of Voronoi Diagrams. 

Definition of a Voronoi diagram and the largest empty circle.

Lynch, Peter. “How Voronoi Diagrams Help Us Understand Our World.” The Irish

Times, 23 Jan. 2017,www.irishtimes.com/news/science/how-voronoi-diagrams-help-us-understand-our-world-1.2947681. 

General background research and examples of application for Voronoi diagrams.

Mount, Dave. “Voronoi Diagrams and Fortune's Algorithm.” cs.umd.edu, 2020,

https://www.cs.umd.edu/class/spring2020/cmsc754/Lects/lect11-vor.pdf. Accessed 2020.

Detailed information on and proof of Fortune's algorithm.

Mumm, Michael. “Voronoi Diagrams.” The Mathematics Enthusiast, vol. 1, no. 2,

2004.    Article 4. 

Mathematical definition of a Voronoi diagram and general background.

O’Rourke. “Voronoi Diagrams and Delaunay Triangulation.” cs.jhu.edu, John Hopkins University,

2016, https://www.cs.jhu.edu/~misha/Spring16/11.pdf. Accessed 2020.

General background and making Voronoi diagrams with a series of perpendicular bisectors.

Setter, Ophir. “Contructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer.” acg.cs, Tel

Aviv University, June 2009, http://acg.cs.tau.ac.il/projects/in-house-projects/vd-via-dc-of-envelopes/exam_presentation.pdf. Accessed December 2020.

Description of the divide and conquer method of producing Voronoi diagrams.

Skiena, Steven. “Voronoi Diagrams.” The Algorithim Design Manual, State University of New York,

June 1997, https://www8.cs.umu.se/kurser/TDBAfl/VT06/algorithms/BOOK/BOOK4/NODE187.HTM. Accessed December 2020.

Description of the incremental algorithm.

Tamassia, Roberto. “Introduction of Voronoi Diagrams.” 22 Mar. 1993. 

Formal definition of a Voronoi diagram.

Thomas, Rachel. “Uncovering the Cause of Cholera.” Plus.maths.org, 12 Feb.

2020,  plus.maths.org/content/uncovering-cause-cholera. 

Connection to cholera outbreak and immunology. Image of map of cholera deaths.

Weisstein, Eric W. "Delaunay Triangulation." From MathWorld--A Wolfram Web Resource.

https://mathworld.wolfram.com/DelaunayTriangulation.html

 

“Delaunay Triangulation.” Wikipedia, Wikimedia Foundation, 13 Dec. 2020,

https://en.wikipedia.org/wiki/Delaunay_triangulation "Voronoi Tessellations." DataGenetics, 01 May 2017, https://datagenetics.com/blog/may12017/index.html

Fortune, Steven. “Voronoi Diagrams and Delaunay Triangulations.” Discrete and Computational

Geometry, CRC Press, 2017, pp. 705 - 721. csun.edu, http://www.csun.edu/~ctoth/Handbook/chap27.pdf. Accessed 2020.

Mitchell, Joseph. “Voronoi and Delaunay Diagrams.” An Introduction to Computational Geometry, State

University of New York, http://www.ams.sunysb.edu/~jsbm/courses/345/13/lecture-Voronoi.pdf. Accessed 2020.

Ringler, Todd. “Introduction to Voronoi Diagrams and Delaunay Triangulations.” Clasp Research, Los

Almos National Laboratory, 2008, http://clasp-research.engin.umich.edu/groups/admg/ASP_Summer_Colloquium/25-Ringler-VoronoiDelaunay.pdf. Accessed 2020.

Wikipedia. “Delaunay Triangulation.” Wikipedia, Wikipedia, 2020,

https://en.wikipedia.org/wiki/Delaunay_triangulation#Applications. Accessed 2020.

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