{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T09:10:14Z","timestamp":1779268214931,"version":"3.51.4"},"publisher-location":"New York, NY, USA","reference-count":25,"publisher":"ACM","license":[{"start":{"date-parts":[[2006,6,5]],"date-time":"2006-06-05T00:00:00Z","timestamp":1149465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2006,6,5]]},"DOI":"10.1145\/1137856.1137891","type":"proceedings-article","created":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T16:53:01Z","timestamp":1153759981000},"page":"227-236","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["The predicates for the Voronoi diagram of ellipses"],"prefix":"10.1145","author":[{"given":"Ioannis Z.","family":"Emiris","sequence":"first","affiliation":[{"name":"National and Kapodistrian University of Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elias P.","family":"Tsigaridas","sequence":"additional","affiliation":[{"name":"National and Kapodistrian University of Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"George M.","family":"Tzoumas","sequence":"additional","affiliation":[{"name":"National and Kapodistrian University of Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2006,6,5]]},"reference":[{"key":"e_1_3_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/3115479.3115811"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/378583.378709"},{"key":"e_1_3_2_1_4_1","volume-title":"Europ. Workshop Comput. Geom","author":"Anton F.","year":"2002","unstructured":"F. Anton , J.-D. Boissonnat , D. Mioc , and M. Yvinec . An exact predicate for the optimal construction of the additively weighted Voronoi diagram . Europ. Workshop Comput. Geom , 2002 .]] F. Anton, J.-D. Boissonnat, D. Mioc, and M. Yvinec. An exact predicate for the optimal construction of the additively weighted Voronoi diagram. Europ. Workshop Comput. Geom, 2002.]]"},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.5555\/1005800.1005803"},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-25944-2_13"},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/11561071_34"},{"key":"e_1_3_2_1_8_1","first-page":"305","volume-title":"Proc. SODA","author":"Boissonnat J.-D.","year":"2003","unstructured":"J.-D. Boissonnat and M. Karavelas . On the combinatorial complexity of Euclidean Voronoi cells and convex hulls of d-dimensional spheres . In Proc. SODA , pages 305 -- 312 , 2003 .]] J.-D. Boissonnat and M. Karavelas. On the combinatorial complexity of Euclidean Voronoi cells and convex hulls of d-dimensional spheres. In Proc. SODA, pages 305--312, 2003.]]"},{"key":"e_1_3_2_1_9_1","volume-title":"Algorithms for Minimization without Derivatives","author":"Brent R.","year":"1973","unstructured":"R. Brent . Algorithms for Minimization without Derivatives . Prentice-Hall , Englewood Cliffs, N.J. , 1973 .]] R. Brent. Algorithms for Minimization without Derivatives. Prentice-Hall, Englewood Cliffs, N.J., 1973.]]"},{"key":"e_1_3_2_1_10_1","series-title":"LNCS","first-page":"254","volume-title":"ESA","author":"Burnikel C.","year":"2001","unstructured":"C. Burnikel , S. Funke , K. Mehlhorn , S. Schirra , and S. Schmitt . A Separation Bound for Real Algebraic Expressions . In ESA , volume 2161 of LNCS , pages 254 -- 265 . Springer , 2001 .]] C. Burnikel, S. Funke, K. Mehlhorn, S. Schirra, and S. Schmitt. A Separation Bound for Real Algebraic Expressions. In ESA, volume 2161 of LNCS, pages 254--265. Springer, 2001.]]"},{"key":"e_1_3_2_1_11_1","volume-title":"Using Algebraic Geometry. Number 185 in GTM","author":"Cox D.","year":"2005","unstructured":"D. Cox , J. Little , and D. O'Shea . Using Algebraic Geometry. Number 185 in GTM . Springer , New York , 2 nd edition, 2005 .]] D. Cox, J. Little, and D. O'Shea. Using Algebraic Geometry. Number 185 in GTM. Springer, New York, 2nd edition, 2005.]]","edition":"2"},{"key":"e_1_3_2_1_12_1","volume-title":"Spec. Issue on Robust Geometric Algorithms and their Implementations, 33(1-2):18--57","author":"Emiris I.Z.","year":"2006","unstructured":"I.Z. Emiris and M.I. Karavelas . The predicates of the Apollonius diagram: algorithmic analysis and implementation. Comp. Geom.: Theory & Appl ., Spec. Issue on Robust Geometric Algorithms and their Implementations, 33(1-2):18--57 , 2006 .]] I.Z. Emiris and M.I. Karavelas. The predicates of the Apollonius diagram: algorithmic analysis and implementation. Comp. Geom.: Theory & Appl., Spec. Issue on Robust Geometric Algorithms and their Implementations, 33(1-2):18--57, 2006.]]"},{"key":"e_1_3_2_1_13_1","first-page":"652","volume-title":"Proc. ESA, LNCS","author":"Emiris I.Z.","year":"2004","unstructured":"I.Z. Emiris and E.P. Tsigaridas . Computing with real algebraic numbers of small degree . In Proc. ESA, LNCS , pages 652 -- 663 . Springer , 2004 .]] I.Z. Emiris and E.P. Tsigaridas. Computing with real algebraic numbers of small degree. In Proc. ESA, LNCS, pages 652--663. Springer, 2004.]]"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/11555964_13"},{"key":"e_1_3_2_1_15_1","first-page":"147","volume-title":"Proc. Europ. Works. Comp. Geom","author":"Emiris I.Z.","year":"2005","unstructured":"I.Z. Emiris and G.M. Tzoumas . Algebraic study of the Apollonius circle of three ellipses . In Proc. Europ. Works. Comp. Geom , pages 147 -- 150 , Holland , 2005 . Also: Poster session, CASC'05, Greece. To appear in SIGSAM Bulletin.]] I.Z. Emiris and G.M. Tzoumas. Algebraic study of the Apollonius circle of three ellipses. In Proc. Europ. Works. Comp. Geom, pages 147--150, Holland, 2005. Also: Poster session, CASC'05, Greece. To appear in SIGSAM Bulletin.]]"},{"key":"e_1_3_2_1_16_1","volume-title":"Comp.-Aided Geom. Design","author":"Etayo F.","year":"2005","unstructured":"F. Etayo , L. Gonzalez-Vega , and N. del Rio . A new approach to characterizing the relative position of two ellipses depending on one parameter . Comp.-Aided Geom. Design , 2005 .]] F. Etayo, L. Gonzalez-Vega, and N. del Rio. A new approach to characterizing the relative position of two ellipses depending on one parameter. Comp.-Aided Geom. Design, 2005.]]"},{"key":"e_1_3_2_1_17_1","first-page":"294","volume-title":"Proc. 17th Canad. Conf. Comp. Geom","author":"Habert L.","year":"2005","unstructured":"L. Habert . Computing bitangents for ellipses . In Proc. 17th Canad. Conf. Comp. Geom , pages 294 -- 297 , 2005 .]] L. Habert. Computing bitangents for ellipses. In Proc. 17th Canad. Conf. Comp. Geom, pages 294--297, 2005.]]"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060244.1060251"},{"key":"e_1_3_2_1_20_1","first-page":"337","volume-title":"Proc. ESA","author":"Karavelas M.I.","year":"2003","unstructured":"M.I. Karavelas and M. Yvinec . Voronoi diagram of convex objects in the plane . In Proc. ESA , pages 337 -- 348 , 2003 .]] M.I. Karavelas and M. Yvinec. Voronoi diagram of convex objects in the plane. In Proc. ESA, pages 337--348, 2003.]]"},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00051-6"},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0925-7721(93)90033-3"},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02716580"},{"key":"e_1_3_2_1_24_1","volume-title":"8th Int. Symposium on Effective Methods in Algebraic Geometry, MEGA","author":"Mourrain B.","year":"2005","unstructured":"B. Mourrain , J. P. Pavone , P. Tr\u00e9buchet , and E. Tsigaridas . SYNAPS, a library for symbolic-numeric computation . In 8th Int. Symposium on Effective Methods in Algebraic Geometry, MEGA , Sardinia, Italy , May 2005 . to appear.]] B. Mourrain, J. P. Pavone, P. Tr\u00e9buchet, and E. Tsigaridas. SYNAPS, a library for symbolic-numeric computation. In 8th Int. Symposium on Effective Methods in Algebraic Geometry, MEGA, Sardinia, Italy, May 2005. to appear.]]"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00049-8"},{"key":"e_1_3_2_1_26_1","series-title":"Lect","volume-title":"Geometric Computation","author":"Yap C.","year":"2004","unstructured":"C. Yap . On guaranteed accuracy computation . In F. Chen and D. Wang, editors, Geometric Computation , volume 11 of Lect . Notes Series Comp. World Scientific , 2004 .]] C. Yap. On guaranteed accuracy computation. In F. Chen and D. Wang, editors, Geometric Computation, volume 11 of Lect. Notes Series Comp. World Scientific, 2004.]]"},{"key":"e_1_3_2_1_27_1","volume-title":"Fundamental Problems of Algorithmic Algebra","author":"Yap C.K.","year":"2000","unstructured":"C.K. Yap . Fundamental Problems of Algorithmic Algebra . Oxford University Press , New York , 2000 .]] C.K. Yap. Fundamental Problems of Algorithmic Algebra. Oxford University Press, New York, 2000.]]"}],"event":{"name":"SoCG06: 22nd Annual Symposium on Computational Geometry","location":"Sedona Arizona USA","acronym":"SoCG06","sponsor":["SIGGRAPH ACM Special Interest Group on Computer Graphics and Interactive Techniques","ACM Association for Computing Machinery","SIGACT ACM Special Interest Group on Algorithms and Computation Theory"]},"container-title":["Proceedings of the twenty-second annual symposium on Computational geometry"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1137856.1137891","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1137856.1137891","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:14:32Z","timestamp":1750259672000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1137856.1137891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6,5]]},"references-count":25,"alternative-id":["10.1145\/1137856.1137891","10.1145\/1137856"],"URL":"https:\/\/doi.org\/10.1145\/1137856.1137891","relation":{},"subject":[],"published":{"date-parts":[[2006,6,5]]},"assertion":[{"value":"2006-06-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}