{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T22:33:19Z","timestamp":1680215599334},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,10,16]],"date-time":"2010-10-16T00:00:00Z","timestamp":1287187200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2010,11]]},"DOI":"10.1007\/s11786-010-0042-5","type":"journal-article","created":{"date-parts":[[2010,10,15]],"date-time":"2010-10-15T09:40:28Z","timestamp":1287135628000},"page":"45-66","source":"Crossref","is-referenced-by-count":12,"title":["Arrangements on Parametric Surfaces I: General Framework and Infrastructure"],"prefix":"10.1007","volume":"4","author":[{"given":"Eric","family":"Berberich","sequence":"first","affiliation":[]},{"given":"Efi","family":"Fogel","sequence":"additional","affiliation":[]},{"given":"Dan","family":"Halperin","sequence":"additional","affiliation":[]},{"given":"Kurt","family":"Mehlhorn","sequence":"additional","affiliation":[]},{"given":"Ron","family":"Wein","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,10,16]]},"reference":[{"key":"42_CR1","unstructured":"The Cgal Project: Cgal User and Reference Manual. Cgal Editorial Board, 3.7 edn. http:\/\/www.cgal.org\/Manual\/3.7\/doc_html\/cgal_manual\/contents.html (2010)"},{"key":"42_CR2","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/B978-044482537-7\/50003-6","volume-title":"Handbook of Computational Geometry, chap. 2","author":"P.K. Agarwal","year":"2000","unstructured":"Agarwal P.K., Sharir M.: Arrangements and their applications. In: Sack, J.-R., Urrutia, J. (eds) Handbook of Computational Geometry, chap. 2, pp. 49\u2013119. Elsevier, Amsterdam (2000)"},{"issue":"3","key":"42_CR3","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1142\/S021819590100050X","volume":"11","author":"M.V.A. Andrade","year":"2001","unstructured":"Andrade M.V.A., Stolfi J.: Exact algorithms for circles on the sphere. Int. J. Comput. Geometry Appl. 11(3), 267\u2013290 (2001)","journal-title":"Int. J. Comput. Geometry Appl."},{"key":"42_CR4","volume-title":"Generic Programming and the STL","author":"M.H. Austern","year":"1999","unstructured":"Austern M.H.: Generic Programming and the STL. Addison-Wesley, New York (1999)"},{"issue":"9","key":"42_CR5","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1109\/TC.1979.1675432","volume":"28","author":"J.L. Bentley","year":"1979","unstructured":"Bentley J.L., Ottmann T.: Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. 28(9), 643\u2013647 (1979)","journal-title":"IEEE Trans. Comput."},{"key":"42_CR6","unstructured":"Berberich, E., Emeliyanenko, P.: Cgal\u2019s curved kernel via analysis. Algorithms for complex shapes. Technical report ACS-TR-123203-04 (2008)"},{"key":"42_CR7","doi-asserted-by":"crossref","unstructured":"Berberich, E., Fogel, E., Halperin, D., Kerber, M., Setter, O.: Arrangements on parametric surfaces II: concretization and applications. Math. Comput. Sci. (2010, accepted)","DOI":"10.1007\/s11786-010-0043-4"},{"key":"42_CR8","doi-asserted-by":"crossref","unstructured":"Berberich, E., Fogel, E., Halperin, D., Mehlhorn, K., Wein, R.: Sweeping and maintaining two-dimensional arrangements on surfaces: a first step. In: Proceedings 15th Annual Eurpean Symposium on Algorithms (ESA), LNCS, vol. 4698, pp. 645\u2013656. Springer-Verlag, Berlin (2007)","DOI":"10.1007\/978-3-540-75520-3_57"},{"key":"42_CR9","doi-asserted-by":"crossref","unstructured":"Berberich, E., Hemmer, M., Kettner, L., Sch\u00f6mer, K., Wolpert, N.: An exact, complete and efficient implementation for computing planar maps of quadric intersection curves. In: Proceedings of 21st Annual Symposium on Computational Geometry (SoCG), pp. 99\u2013106. ACM Press, New York (2005)","DOI":"10.1145\/1064092.1064110"},{"key":"42_CR10","doi-asserted-by":"crossref","unstructured":"Berberich, E., Kerber, M.: Exact arrangements on tori and Dupin cyclides. In: Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling (SPM), pp. 59\u201366. ACM Press, New York (2008)","DOI":"10.1145\/1364901.1364912"},{"key":"42_CR11","doi-asserted-by":"crossref","unstructured":"Brisson, E.: Representing geometric structures in d dimensions: topology and order. In: SCG \u201989: Proceedings of the Fifth Annual Symposium on Computational Geometry, pp. 218\u2013227. ACM, New York (1989)","DOI":"10.1145\/73833.73858"},{"issue":"6\u20137","key":"42_CR12","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.comgeo.2008.10.004","volume":"42","author":"F. Cazals","year":"2009","unstructured":"Cazals F., Loriot S.: Computing the arrangement of circles on a sphere, with applications in structural biology. Comput. Geom. Theory Appl. 42(6\u20137), 551\u2013565 (2009)","journal-title":"Comput. Geom. Theory Appl."},{"issue":"6\u20137","key":"42_CR13","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.comgeo.2008.10.004","volume":"42","author":"F. Cazals","year":"2009","unstructured":"Cazals F., Loriot S.: Computing the arrangement of circles on a sphere, with applications in structural biology. Comput. Geom. Theory Appl. 42(6\u20137), 551\u2013565 (2009)","journal-title":"Comput. Geom. Theory Appl."},{"issue":"6\u20137","key":"42_CR14","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.comgeo.2008.10.003","volume":"42","author":"P.M.M. Castro de","year":"2009","unstructured":"de Castro P.M.M., Cazals F., Loriot S., Teillaud M.: Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere. Comput. Geom. Theory Appl. 42(6\u20137), 536\u2013550 (2009)","journal-title":"Comput. Geom. Theory Appl."},{"key":"42_CR15","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF02187681","volume":"1","author":"H. Edelsbrunner","year":"1986","unstructured":"Edelsbrunner H., Seidel R.: Voronoi diagrams and arrangements. Disc. Comput. Geom. 1, 25\u201344 (1986)","journal-title":"Disc. Comput. Geom."},{"key":"42_CR16","unstructured":"Eigenwillig, A., Kerber, M.: Exact and efficient 2D-arrangements of arbitrary algebraic curves. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 122\u2013131, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics (SIAM) (2008)"},{"issue":"11","key":"42_CR17","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1002\/1097-024X(200009)30:11<1167::AID-SPE337>3.0.CO;2-B","volume":"30","author":"A. Fabri","year":"2000","unstructured":"Fabri A., Giezeman , Lutz Kettner G.-J., Schirra S., Sch\u00f6nherr S.: On the design of Cgal a computational geometry algorithms library. Softw. Pract. Exp. 30(11), 1167\u20131202 (2000)","journal-title":"Softw. Pract. Exp."},{"key":"42_CR18","first-page":"1","volume-title":"Effective Computational Geometry for Curves and Surfaces, chap. 1","author":"E. Fogel","year":"2007","unstructured":"Fogel E., Halperin D., Kettner L., Teillaud M., Wein R., Wolpert N.: Arrangements. In: Boissonnat, J.-D., Teillaud, M. (eds) Effective Computational Geometry for Curves and Surfaces, chap. 1, pp. 1\u201366. Springer-Verlag, Berlin (2007)"},{"key":"42_CR19","doi-asserted-by":"crossref","unstructured":"Fogel, E., Setter, O., Halperin, D.: Exact implementation of arrangements of geodesic arcs on the sphere with applications. In: Abstracts of the 24th European Workshop on Computational Geometry, pp. 83\u201386 (2008)","DOI":"10.1145\/1377676.1377711"},{"key":"42_CR20","doi-asserted-by":"crossref","unstructured":"Fogel, E., Setter, O., Halperin, D.: Movie: Arrangements of geodesic arcs on the sphere. In: Proceedings of 24th Annual ACM Symposium on Computational Geometry (SoCG), pp. 218\u2013219. ACM Press, New York (2008)","DOI":"10.1145\/1377676.1377711"},{"key":"42_CR21","volume-title":"Design Patterns\u2014Elements of Reusable Object-Oriented Software","author":"E. Gamma","year":"1999","unstructured":"Gamma E., Helm R., Johnson R., Vlissides J.: Design Patterns\u2014Elements of Reusable Object-Oriented Software. Addison-Wesley, New York (1999)"},{"key":"42_CR22","doi-asserted-by":"crossref","unstructured":"Halperin, D.: Arrangements. In: Goodman, J.E., O\u2019Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, chap. 24, 2nd edn., pp. 529\u2013562. Chapman & Hall\/CRC (2004)","DOI":"10.1201\/9781420035315.ch24"},{"key":"42_CR23","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0925-7721(98)00014-5","volume":"10","author":"D. Halperin","year":"1998","unstructured":"Halperin D., Shelton C.R.: A perturbation scheme for spherical arrangements with application to molecular modeling. Comput. Geom. Theory. Appl. 10, 273\u2013287 (1998)","journal-title":"Comput. Geom. Theory. Appl."},{"key":"42_CR24","unstructured":"Hemmer, M.: Exact computation of the adjacency graph of an arrangement of quadrics. Ph.D. thesis, Johannes-Gutenberg-Universit\u00e4t, Mainz, Germany (2008)"},{"key":"42_CR25","unstructured":"Hijazi, Y.O., Breuel, T.M.: Computing arrangements using subdivision and interval arithmetic. In: Proceedings of 6th International Conference on Curves and Surfaces, pp. 173\u2013182 (2006)"},{"key":"42_CR26","doi-asserted-by":"crossref","unstructured":"Lazarus, F., Pocchiola, M., Vegter, G., Verroust, A.: Computing a canonical polygonal schema of an orientable triangulated surface. In: Proceedings of 17th Annual ACM Symposium on Computational Geometry (SoCG), pp. 80\u201389 (2001)","DOI":"10.1145\/378583.378630"},{"key":"42_CR27","unstructured":"Mehlhorn, K., N\u00e4her, S.: Leda: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (2000)"},{"issue":"3","key":"42_CR28","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1142\/S0218195903001141","volume":"13","author":"K. Mehlhorn","year":"2003","unstructured":"Mehlhorn K., Seel M.: Infimaximal frames: A technique for making lines look like segments. Int. J. Comput. Geometry Appl. 13(3), 241\u2013255 (2003)","journal-title":"Int. J. Comput. Geometry Appl."},{"key":"42_CR29","doi-asserted-by":"crossref","unstructured":"Meyerovitch, M.: Robust, generic and efficient construction of envelopes of surfaces in three-dimensional space. In: Proceedings of 14th Annual European Symposium on Algorithms (ESA), LNCS, vol. 4168, pp. 792\u2013803. Springer-Verlag, Berlin (2006)","DOI":"10.1007\/11841036_70"},{"issue":"2","key":"42_CR30","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1142\/S021819590700229X","volume":"17","author":"V. Milenkovic","year":"2007","unstructured":"Milenkovic V., Sacks E.: An approximate arrangement algorithm for semi-algebraic curves. Int. J. Comput. Geom. Appl. 17(2), 175\u2013198 (2007)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"42_CR31","doi-asserted-by":"crossref","unstructured":"Setter, O., Sharir, M., Halperin, D.: Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space. In: Proceedings of 6th Annual International Symposium on Voronoi Diagrams in Science and Engineering (ISVD), pp. 43\u201352 (2009)","DOI":"10.1109\/ISVD.2009.20"},{"issue":"1\u20132","key":"42_CR32","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.comgeo.2006.11.007","volume":"38","author":"R. Wein","year":"2007","unstructured":"Wein R., Fogel E., Zukerman B., Halperin D.: Advanced programming techniques applied to Cgal\u2019s arrangement package. Comput. Geom. Theory Appl. 38(1\u20132), 37\u201363 (2007) Special issue on Cgal","journal-title":"Comput. Geom. Theory Appl."},{"key":"42_CR33","unstructured":"Wein, R., Fogel, E., Zukerman, B., Halperin, D.: 2D arrangements. In: Cgal User and Reference Manual. Cgal Editorial Board, 3.7 edn. http:\/\/www.cgal.org\/Manual\/3.7\/doc_html\/cgal_manual\/packages.html#Pkg:Arrangements2 (2010)"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-010-0042-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-010-0042-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-010-0042-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T14:24:07Z","timestamp":1559744647000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-010-0042-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,16]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,11]]}},"alternative-id":["42"],"URL":"https:\/\/doi.org\/10.1007\/s11786-010-0042-5","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,16]]}}}