000151346 001__ 151346 000151346 005__ 20210129213449.0 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 000151346 3367_ $$2DataCite$$aOutput Types/Journal article 000151346 3367_ $$00$$2EndNote$$aJournal Article 000151346 3367_ $$2BibTeX$$aARTICLE 000151346 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000151346 3367_ $$2DRIVER$$aarticle 000151346 520__ $$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. 000151346 536__ $$0G:(DE-HGF)POF2-411$$a411 - Computational Science and Mathematical Methods (POF2-411)$$cPOF2-411$$fPOF II$$x0 000151346 588__ $$aDataset connected to CrossRef, juser.fz-juelich.de 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$$y2012 000151346 8564_ $$uhttps://juser.fz-juelich.de/record/151346/files/FZJ-2014-01319.pdf$$yRestricted$$zPublished final document. 000151346 909CO $$ooai:juser.fz-juelich.de:151346$$pVDB 000151346 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)132077$$aForschungszentrum Jülich GmbH$$b1$$kFZJ 000151346 9132_ $$0G:(DE-HGF)POF3-511$$1G:(DE-HGF)POF3-510$$2G:(DE-HGF)POF3-500$$aDE-HGF$$bKey Technologies$$lSupercomputing & Big Data $$vComputational Science and Mathematical Methods$$x0 000151346 9131_ $$0G:(DE-HGF)POF2-411$$1G:(DE-HGF)POF2-410$$2G:(DE-HGF)POF2-400$$3G:(DE-HGF)POF2$$4G:(DE-HGF)POF$$aDE-HGF$$bSchlüsseltechnologien$$lSupercomputing$$vComputational Science and Mathematical Methods$$x0 000151346 9141_ $$y2013 000151346 915__ $$0StatID:(DE-HGF)0020$$2StatID$$aNo Peer Review 000151346 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS 000151346 915__ $$0StatID:(DE-HGF)0420$$2StatID$$aNationallizenz 000151346 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0 000151346 980__ $$ajournal 000151346 980__ $$aVDB 000151346 980__ $$aUNRESTRICTED 000151346 980__ $$aI:(DE-Juel1)JSC-20090406