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Some algorithms for polygons on a sphere

Show simple item record Chamberlain, Robert G. Duquette, William H. 2007-09-13T18:08:10Z 2007-09-13T18:08:10Z 2007-06
dc.identifier.clearanceno 07-03
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
dc.description.sponsorship NASA/JPL en
dc.format.extent 2428415 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US en
dc.publisher Pasadena, CA : Jet Propulsion Laboratory en
dc.relation.ispartofseries JPL Publication en
dc.relation.ispartofseries 07-03 en
dc.subject algorithms en
dc.subject applied mathematics en
dc.subject geographical information systems (GIS) en
dc.subject maps en
dc.subject rhumb lines en
dc.subject spherical geometry en
dc.title Some algorithms for polygons on a sphere en
dc.type Technical Report en

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