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Some algorithms for polygons on a sphere.

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dc.contributor.author Chamberlain, Robert G.
dc.contributor.author Duquette, William H.
dc.date.accessioned 2009-04-24T19:58:21Z
dc.date.available 2009-04-24T19:58:21Z
dc.date.issued 2007-04-17
dc.identifier.citation Association of American Geographers Annual Meeting, San Francisco, California, April 17-21, 2007. en_US
dc.identifier.clearanceno 07-0286
dc.identifier.uri http://hdl.handle.net/2014/41271
dc.description.abstract A limited search for polygon algorithms for use in a new military training simulation that interfaces with several others produced only planar algorithms. To avoid having to implement several different sophisticated map projections to guarantee compatibility with all the other simulations, we opted to develop algorithms that work directly on a sphere. The first is an algorithm to compute the area of a polygon whose edges are segments of great circles. Since our model represents certain object locations as mathematical points, the second topic is whether a specified point is inside a specified polygon. Possibly pathological cases are identified and eliminated. When we realized that most political boundaries are actually rhumb lines, use of the Mercator projection equations seemed unavoidable. We then reasoned that if all the edges were short enough, lat-lon lines, great circle segments, and rhumb lines would be close enough to being identical that we could use whichever was most convenient. Thence, we looked at the relationship between the maximum distances between great circle segments and rhumb lines and between lat-lon lines and rhumb lines as functions of length, azimuth, and latitude. The final algorithm finds the area overlapped by two polygons. Again, potentially pathological cases are identified and eliminated. en_US
dc.description.sponsorship NASA/JPL en_US
dc.language.iso en_US en_US
dc.publisher Pasadena, CA : Jet Propulsion Laboratory, National Aeronautics and Space Administration, 2007. en_US
dc.subject GIS en_US
dc.subject algorithms en_US
dc.subject spherical geometry en_US
dc.subject polygons en_US
dc.subject areas en_US
dc.title Some algorithms for polygons on a sphere. en_US
dc.type Preprint en_US


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