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000151346 0247_ $$2doi$$a10.1007/s00791-013-0214-3
000151346 0247_ $$2ISSN$$a1433-0369
000151346 0247_ $$2ISSN$$a1432-9360
000151346 037__ $$aFZJ-2014-01319
000151346 082__ $$a570
000151346 1001_ $$0P:(DE-HGF)0$$aHughes, Gary B.$$b0$$eCorresponding author
000151346 245__ $$aCalculating ellipse overlap areas
000151346 260__ $$aBerlin$$bSpringer$$c2012
000151346 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1392719695_30879
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000151346 520__ $$aWe present an approach for finding the overlap area between two ellipses that does not rely on proxy curves. The Gauss-Green formula is used to determine a segment area between two points on an ellipse. Overlap between two ellipses is calculated by combining the areas of appropriate segments and polygons in each ellipse. For four of the ten possible orientations of two ellipses, the method requires numerical determination of transverse intersection points. Approximate intersection points can be determined by solving the two implicit ellipse equations simultaneously. Alternative approaches for finding transverse intersection points are available using tools from algebraic geometry, e.g., based on solving an Eigen-problem that is related to companion matrices of the two implicit ellipse curves. Implementations in C of several algorithm options are analyzed for accuracy, precision and robustness with a range of input ellipses.
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000151346 7001_ $$0P:(DE-Juel1)132077$$aChraibi, Mohcine$$b1$$ufzj
000151346 773__ $$0PERI:(DE-600)1458972-2$$a10.1007/s00791-013-0214-3$$gVol. 15, no. 5, p. 291 - 301$$n5$$p291 - 301$$tComputing and visualization in science$$v15$$x1433-0369$$y2012
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000151346 9141_ $$y2013
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