{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T13:30:09Z","timestamp":1726407009142},"reference-count":25,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[2001,5,1]],"date-time":"2001-05-01T00:00:00Z","timestamp":988675200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Graphical Models"],"published-print":{"date-parts":[[2001,5]]},"DOI":"10.1006\/gmod.2001.0539","type":"journal-article","created":{"date-parts":[[2002,9,17]],"date-time":"2002-09-17T18:31:03Z","timestamp":1032287463000},"page":"163-175","source":"Crossref","is-referenced-by-count":15,"title":["Topological and Geometric Properties of Interval Solid Models"],"prefix":"10.1006","volume":"63","author":[{"given":"T.","family":"Sakkalis","sequence":"first","affiliation":[]},{"given":"G.","family":"Shen","sequence":"additional","affiliation":[]},{"given":"N.M.","family":"Patrikalakis","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1006\/gmod.2001.0539_RF1","doi-asserted-by":"crossref","unstructured":"T. J. Peters, N. F. Stewart, D. R. Ferguson, and P. S. Fussel, Algorithmic tolerances and semantics in data exchange, in Proceedings of the 13th ACM Symposium on Computational Geometry, June 1997, Nice, France, pp. 403\u2013405.","DOI":"10.1145\/262839.263027"},{"key":"10.1006\/gmod.2001.0539_RF2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/2.16223","article-title":"The problems of accuracy and robustness in geometric computation","volume":"22","author":"Hoffmann","year":"1989","journal-title":"Computer"},{"journal-title":"Geometric and Solid Modeling\u2014An Introduction","year":"1989","author":"Hoffmann","key":"10.1006\/gmod.2001.0539_RF3"},{"key":"10.1006\/gmod.2001.0539_RF4","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/0010-4485(93)90071-U","article-title":"Robust polygon modeling","volume":"25","author":"Milenkovic","year":"1993","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF5","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0010-4485(96)00041-3","article-title":"Polyhedral modeling with multiprecision integer arithmet","volume":"29","author":"Fortune","year":"1997","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF6","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/S0167-8396(99)00032-1","article-title":"Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic: I\u2013representations","volume":"16","author":"Keyser","year":"1999","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1006\/gmod.2001.0539_RF7","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0167-8396(99)00033-3","article-title":"Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic: II\u2013computation","volume":"16","author":"Keyser","year":"1999","journal-title":"Comput. Aided Geom. Design"},{"key":"10.1006\/gmod.2001.0539_RF8","first-page":"208","article-title":"Epsilon geometry: Building robust algorithms from imprecise computations","author":"Salesin","year":"1989","journal-title":"Proceedings of the 5th ACM Annual Symposium on Computational Geometry"},{"journal-title":"Epsilon Geometry: Building Robust Algorithms from Imprecise Computations","year":"1991","author":"Salesin","key":"10.1006\/gmod.2001.0539_RF9"},{"key":"10.1006\/gmod.2001.0539_RF10","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/0010-4485(96)00013-9","article-title":"Robust interval solid modeling: Part I, representations","volume":"28","author":"Hu","year":"1996","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF11","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/0010-4485(96)00014-0","article-title":"Robust interval solid modeling: Part II, boundary evaluation","volume":"28","author":"Hu","year":"1996","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF12","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0010-4485(94)90063-9","article-title":"Error-free boundary evaluation based on a lazy rational arithmetic: A detailed implementation","volume":"26","author":"Benouamer","year":"1994","journal-title":"Comput. Aided Design"},{"journal-title":"A General Approach to the Design of Robust Algorithms for Geometric Modeling","year":"1995","author":"Agrawal","key":"10.1006\/gmod.2001.0539_RF13"},{"key":"10.1006\/gmod.2001.0539_RF14","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/0010-4485(95)00063-1","article-title":"Robust interval algorithm for curve intersections","volume":"28","author":"Hu","year":"1996","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF15","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/S0010-4485(96)00099-1","article-title":"Robust interval algorithm for surface intersections","volume":"29","author":"Hu","year":"1997","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF16","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/S0010-4485(97)00086-9","article-title":"Efficient and reliable methods for rounded interval arithmetic","volume":"30","author":"Abrams","year":"1998","journal-title":"Comput. Aided Design"},{"journal-title":"Topology: A First Course","year":"1975","author":"Munkres","key":"10.1006\/gmod.2001.0539_RF17"},{"journal-title":"Stable Mappings and Their Singularities","year":"1980","author":"Golubitsky","key":"10.1006\/gmod.2001.0539_RF18"},{"journal-title":"Lectures on Algebraic Topology","year":"1967","author":"Greenberg","key":"10.1006\/gmod.2001.0539_RF19"},{"key":"10.1006\/gmod.2001.0539_RF20","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/S0010-4485(00)00047-6","article-title":"Representational validity of boundary representation models","volume":"32","author":"Sakkalis","year":"2000","journal-title":"Comput. Aided Design"},{"key":"10.1006\/gmod.2001.0539_RF21","first-page":"140","article-title":"Interval methods for B-rep model verification and rectification","author":"Shen","year":"2000","journal-title":"Proceedings of ASME 2000 IDETC\/CIE, 2000 ASME Design Automation Conference, Baltimore, MD, September 2000"},{"key":"10.1006\/gmod.2001.0539_RF22","unstructured":"G. Shen, T. Sakkalis, and N. M. Patrikalakis, Manifold boundary representation model rectification, in Proceedings of the 3rd International Conference on Integrated Design and Manufacturing in Mechanical EngineeringC. Mascle, C. Fortin, and J. Pegna, Eds., p. 199. [CDROM, Montreal, QC, Canada, May 2000, Presses Internationales Polytechnique, Montreal, Canada, May 2000]"},{"key":"10.1006\/gmod.2001.0539_RF23","doi-asserted-by":"crossref","unstructured":"N. M. Patrikalakis, T. Sakkalis, and G. Shen, Boundary representation models: Validity and rectification, in Proceedings of the 9th IMA Conference on the Mathematics of Surfaces, University of Cambridge, UK, September 2000R. Cipolla and R. Martin, Eds., pp. 389\u2013409, Springer-Verlag, London, 2000.","DOI":"10.1007\/978-1-4471-0495-7_23"},{"journal-title":"Interval Analysis","year":"1966","author":"Moore","key":"10.1006\/gmod.2001.0539_RF24"},{"key":"10.1006\/gmod.2001.0539_RF25","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1142\/S0218654398000040","article-title":"Numerical and geometric properties of interval B-splines","volume":"4","author":"Shen","year":"1998","journal-title":"Internat. J. Shape Model."}],"container-title":["Graphical Models"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1524070301905399?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1524070301905399?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,12,16]],"date-time":"2019-12-16T18:17:23Z","timestamp":1576520243000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1524070301905399"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,5]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,5]]}},"alternative-id":["S1524070301905399"],"URL":"https:\/\/doi.org\/10.1006\/gmod.2001.0539","relation":{},"ISSN":["1524-0703"],"issn-type":[{"type":"print","value":"1524-0703"}],"subject":[],"published":{"date-parts":[[2001,5]]}}}