{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T07:01:08Z","timestamp":1773471668301,"version":"3.50.1"},"reference-count":8,"publisher":"International Electronic Journal of Geometry, Person (Kazim ILARSLAN)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2024,1,7]]},"abstract":"<jats:p xml:lang=\"en\">This work aims to classify the families of curves obtained by the intersection of an arbitrary hyperbolic cylinder with an arbitrary torus sharing the same center, based on the number of their connected components and the number of their self-intersections points. The graphic geometric representation of these curves, in GeoGebra, and the respective algebraic descriptions, supported from a theoretical and computational point of view, are of fundamental importance for the development of this work. In this paper, we describe the procedure and the necessary implementation to achieve the outlined objective.<\/jats:p>","DOI":"10.36890\/iejg.1318186","type":"journal-article","created":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T12:06:03Z","timestamp":1726488363000},"page":"336-347","source":"Crossref","is-referenced-by-count":1,"title":["The Intersection Curve of an Hyperbolic Cylinder with a Torus Sharing the Same Center"],"prefix":"10.36890","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7076-707X","authenticated-orcid":true,"given":"Ana","family":"Breda","sequence":"first","affiliation":[{"name":"University of Aveiro"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5589-8100","authenticated-orcid":true,"given":"Alexandre","family":"Trocado","sequence":"additional","affiliation":[{"name":"CIDMA - Center for Research & Development in Mathematics and Applications"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6830-6503","authenticated-orcid":true,"given":"Jos\u00e9 Manuel","family":"Dos Santos","sequence":"additional","affiliation":[{"name":"University of Coimbra"}]}],"member":"22972","published-online":{"date-parts":[[2024,10,27]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"[1] Breda, A. M., Trocado, A., Dos Santos, J. M.: The intersection curve of an ellipsoid with a torus sharing the same center. In: Proceedings\r\nof the 20th International Conference on Geometry and Graphics (ICGG2022), 127-137. Springer International Publishing (2023).\r\nhttps:\/\/doi.org\/10.1007\/978-3-031-13588-0_11","DOI":"10.1007\/978-3-031-13588-0_11"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"[2] Breda, A. M., Trocado, A., Dos Santos, J. M.: Torus and quadrics intersection using GeoGebra. In: Proceedings of the 19th International\r\nConference on Geometry and Graphics (ICGG2020), 484-493. Springer International Publishing (2021). https:\/\/doi.org\/10.1007\/978-3-\r\n030-63403-2_43","DOI":"10.1007\/978-3-030-63403-2_43"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"[3] Gonzalez-Vega, L., Trocado, A.: Using maple to compute the intersection curve of two quadrics: Improving the intersectplot command. Maple in\r\nMathematics Education and Research, 92-100. Springer International Publishing (2020). https:\/\/doi.org\/10.1007\/978-3-030-41258-6_7","DOI":"10.1007\/978-3-030-41258-6_7"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"[4] Gonzalez-Vega, L., Trocado, A.: Tools for analyzing the intersection curve between two quadrics through projection and lifting. Journal of\r\nComputational and Applied Mathematics, 393, 113522 (2021). https:\/\/doi.org\/10.1016\/j.cam.2021.113522","DOI":"10.1016\/j.cam.2021.113522"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"[5] Kim, K., Kim, M., Oh, K.: Torus\/sphere intersection based on a configuration space approach. Graphical Models and Image Processing, 60 (1),\r\n77\u201392 (1998). https:\/\/doi.org\/10.1006\/gmip.1997.0451","DOI":"10.1006\/gmip.1997.0451"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"[6] Pironti, A., Walker, M.: Fusion, tokamaks, and plasma control: an introduction and tutorial. IEEE Control Systems Magazine, 25 (5), 30\u201343\r\n(2005). https:\/\/10.0.4.85\/MCS.2005.1512794","DOI":"10.1109\/MCS.2005.1512794"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"[7] Gonzalez-Vega, L., Trocado, A., Dos Santos, J. M.: Intersecting two quadrics with GeoGebra. Algebraic Informatics, 237-248. Springer\r\nInternational Publishing (2019). https:\/\/doi.org\/10.1007\/978-3-030-21363-3_20","DOI":"10.1007\/978-3-030-21363-3_20"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"[8] Gonzalez-Vega, L.: A subresultant theory for multivariate polynomials. In: Proceedings of the International Symposium on Symbolic and\r\nAlgebraic Computation (ISSAC\u201991), 79-85. ACM (1991).","DOI":"10.1145\/120694.120705"}],"container-title":["International Electronic Journal of Geometry"],"original-title":[],"deposited":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T22:40:36Z","timestamp":1747953636000},"score":1,"resource":{"primary":{"URL":"http:\/\/dergipark.org.tr\/en\/doi\/10.36890\/iejg.1318186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,27]]},"references-count":8,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,10,27]]}},"URL":"https:\/\/doi.org\/10.36890\/iejg.1318186","relation":{},"ISSN":["1307-5624"],"issn-type":[{"value":"1307-5624","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,27]]}}}