{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T13:06:36Z","timestamp":1775307996241,"version":"3.50.1"},"reference-count":26,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-113192GB-I00"],"award-info":[{"award-number":["PID2020-113192GB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer Aided Geometric Design"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1016\/j.cagd.2026.102533","type":"journal-article","created":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T17:01:45Z","timestamp":1773421305000},"page":"102533","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting"],"prefix":"10.1016","volume":"126","author":[{"given":"Jorge","family":"Caravantes","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8652-4312","authenticated-orcid":false,"given":"Gema M.","family":"Diaz-Toca","sequence":"additional","affiliation":[]},{"given":"Mario","family":"Fioravanti","sequence":"additional","affiliation":[]},{"given":"Laureano","family":"Gonzalez-Vega","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"6","key":"10.1016\/j.cagd.2026.102533_bib0005","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/j.jsc.2005.01.006","article-title":"Computation of the topology of real algebraic space curves","volume":"39","author":"Alc\u00e1zar","year":"2005","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.cagd.2026.102533_bib0010","series-title":"Proceedings of the Twenty-First Annual Symposium on Computational Geometry, SCG 2005, ACM","first-page":"99","article-title":"An exact, complete and efficient implementation for computing planar maps of quadric intersection curves","author":"Berberich","year":"2005"},{"issue":"4","key":"10.1016\/j.cagd.2026.102533_bib0015","article-title":"Algebraic curves on a torus","volume":"77","author":"Bottema","year":"1974","journal-title":"Indag. Math. (Proc.)"},{"key":"10.1016\/j.cagd.2026.102533_bib0020","series-title":"ICGG 2020 - Proceedings of the 19th International Conference on Geometry and Graphics. ICGG 2021. Advances in Intelligent Systems and Computing","article-title":"Torus and quadrics intersection using GeoGebra","volume":"vol. 1296","author":"Breda","year":"2021"},{"key":"10.1016\/j.cagd.2026.102533_bib0025","series-title":"ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. Lecture Notes on Data Engineering and Communications Technologies","article-title":"The intersection curve of an ellipsoid with a torus sharing the same center","volume":"vol. 146","author":"Breda","year":"2023"},{"issue":"2","key":"10.1016\/j.cagd.2026.102533_bib0030","doi-asserted-by":"crossref","first-page":"336","DOI":"10.36890\/iejg.1318186","article-title":"The intersection curve of an hyperbolic cylinder with a torus sharing the same center","volume":"17","author":"Breda","year":"2024","journal-title":"Int. Electron. J. Geom."},{"issue":"265","key":"10.1016\/j.cagd.2026.102533_bib0035","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1090\/S0025-5718-08-02111-X","article-title":"Explicit factors of some iterated resultants and discriminants","volume":"78","author":"Bus\u00e9","year":"2009","journal-title":"Math. Comput."},{"key":"10.1016\/j.cagd.2026.102533_bib0040","doi-asserted-by":"crossref","DOI":"10.1016\/j.jsc.2024.102309","article-title":"An improved complexity bound for computing the topology of a real algebraic space curve","volume":"125","author":"Cheng","year":"2024","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.cagd.2026.102533_bib0045","series-title":"Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-16721-3","author":"Cox","year":"2015","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319167206"},{"key":"10.1016\/j.cagd.2026.102533_bib0050","series-title":"ISSAC\u201908: Proceedings of the Twenty-First International Symposium on Symbolic and Algebraic Computation","first-page":"54","article-title":"On the computation of the topology of a Non-Reduced implicit space curve","author":"Daouda","year":"2008"},{"key":"10.1016\/j.cagd.2026.102533_bib0055","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.jsc.2007.10.006","article-title":"Near-optimal parameterization of the intersection of quadrics: i. The generic algorithm","volume":"43","author":"Dupont","year":"2008","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.cagd.2026.102533_bib0060","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.jsc.2007.10.012","article-title":"Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils","volume":"43","author":"Dupont","year":"2008","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.cagd.2026.102533_bib0065","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.jsc.2007.10.007","article-title":"Near-optimal parameterization of the intersection of quadrics: III. Parameterizing singular intersections","volume":"43","author":"Dupont","year":"2008","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.cagd.2026.102533_bib0070","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/j.cagd.2009.07.003","article-title":"Solving the implicitization, inversion and reparametrization problems for rational curves through subresultants","volume":"26","author":"Gonzalez-Vega","year":"2009","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.cagd.2026.102533_bib0075","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2021.113522","article-title":"Tools for analyzing the intersection curve between two quadrics through projection and lifting","volume":"393","author":"Gonzalez-Vega","year":"2021","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cagd.2026.102533_bib0080","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.cagd.2012.10.001","article-title":"Topological classification of non-degenerate intersections of two ring tori","volume":"30","author":"Jia","year":"2013","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.cagd.2026.102533_bib0085","series-title":"Proc. Of Israel-Korea Bi National Conference on New Themes in Computerized Geometrical Modeling Tel-Aviv","article-title":"Computing all conic sections in torus and natural quadric intersections","author":"Kim","year":"1998"},{"key":"10.1016\/j.cagd.2026.102533_bib0090","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1006\/gmip.1997.0451","article-title":"Torus\/sphere intersection based on a configuration space approach","volume":"1","author":"Kim","year":"1998","journal-title":"Graph. Models Image Process."},{"key":"10.1016\/j.cagd.2026.102533_bib0095","series-title":"Torus and Simple Surface Intersection Based on a Configuration Space Approach","author":"Kim","year":"1998"},{"key":"10.1016\/j.cagd.2026.102533_bib0100","series-title":"Introduction to Plane Algebraic Curves","author":"Kunz","year":"2005"},{"issue":"6","key":"10.1016\/j.cagd.2026.102533_bib0105","first-page":"225","article-title":"Sur l\u2019intersection d\u2019un TORE ET d\u2019une quadrique","volume":"2","author":"Lebesgue","year":"1927","journal-title":"Nouv. Ann. de Math."},{"key":"10.1016\/j.cagd.2026.102533_bib0110","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1080\/16864360.2004.10738288","article-title":"Algebraic algorithms for computing intersections between torus and natural quadrics","volume":"1","author":"Li","year":"2004","journal-title":"Comput.-Aided Des. Appl."},{"key":"10.1016\/j.cagd.2026.102533_bib0115","series-title":"Algorithmic Algebra","author":"Mishra","year":"1993"},{"key":"10.1016\/j.cagd.2026.102533_bib0120","author":"Moroni"},{"key":"10.1016\/j.cagd.2026.102533_bib0125","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.comgeo.2004.02.007","article-title":"An exact and efficient approach for computing a cell in an arrangement of quadrics","volume":"33","author":"Schomer","year":"2006","journal-title":"Comput. Geom. Theory Appl."},{"issue":"102244","key":"10.1016\/j.cagd.2026.102533_bib0130","article-title":"Topological classification of the intersection curves of two quadrics using a set of discriminants","volume":"107","author":"Shao","year":"2023","journal-title":"Comput. Aided Geom. Des."}],"container-title":["Computer Aided Geometric Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167839626000269?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167839626000269?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T12:11:40Z","timestamp":1775304700000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167839626000269"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":26,"alternative-id":["S0167839626000269"],"URL":"https:\/\/doi.org\/10.1016\/j.cagd.2026.102533","relation":{},"ISSN":["0167-8396"],"issn-type":[{"value":"0167-8396","type":"print"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting","name":"articletitle","label":"Article Title"},{"value":"Computer Aided Geometric Design","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cagd.2026.102533","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"102533"}}