# 2008, 2001, English, Map, Video edition: Bisectors, Buffers, and Base Maps Arlinghaus, Sandra Lach; Arlinghaus, S. L.

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Physical Description
• 169857 bytes, application/​zip
• Animation
• Article
• Image
Published
• Institute of Mathematical Geography
• 2008-05-06T01:13:08Z
• 2001-12-21
Language
• English

### Edition details

Title
• Bisectors, Buffers, and Base Maps
Creator
• Arlinghaus, Sandra Lach
• Arlinghaus, S. L.
Other Creators
• Adjunct Professor of Mathematical Geography and Population-Environment Dynamics
• School of Natural Resources and Environment
• Community Systems Foundation
• Arlinghaus Enterprises
• Ann Arbor
Published
• Institute of Mathematical Geography
• 2008-05-06T01:13:08Z
• 2001-12-21
Physical Description
• 169857 bytes, application/​zip
• Animation
• Article
• Image
Subjects
Notes
• Once the file is unzipped, launch index.html in an internet browser window.
• In 1911, Thiessen and Alter [21] wrote on the analysis of rainfall using polygons surrounding rain gauges. Given a scatter of rain gauges, represented abstractly as dots, partition the underlying plane into polygons containing the dots in such a way that all points within any given polygon are closer to the rain gauge dot within that polygon than they are to any other gauge-dot. The geometric construction usually associated with performing this partition of the plane into a mutually exclusive, yet exhaustive, set of polygons is performed by joining the gauge-dots with line segments, finding the perpendicular bisectors of those segments, and extracting a set of polygons with sides formed by perpendicular bisectors. It is this latter set of polygons that has come to be referred to as "Thiessen polygons" (and earlier names such as Dirichlet region or Voronoi polygon, see Coxeter [4]). The construction using bisectors is tedious and difficult to execute with precision when performed by hand. Kopec (1963) [11] noted that an equivalent construction results when circles of radius the distance between adjacent points are used. Indeed, that construction is but one case of a general construction of Euclid. Like Kopec, Rhynsburger (1973) [20] also sought easier ways to construct Thiessen polygons: Kopec through knowledgeable use of geometry and Rhynsburger through the development of computer algorithms. The world of the Geographical Information System (GIS) software affords an opportunity to combine both.
• Peer Reviewed
• http:/​/​deepblue.lib.umich.edu/​bitstream/​2027.42/​58352/​1/​sarhaus.zip
• Solstice, Volume XII, Number 2
• Arlinghaus, Sandra L. "Bisectors, Buffers, and Base Maps." Solstice: An Electronic Journal of Geography and Mathematics, Volume XII, Number 2. Ann Arbor: Institute of Mathematical Geography, 2001. Persistent URL (URI): http:/​/​hdl.handle.net/​2027.42/​58352
• 1059-5325
Language
• English
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