{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T09:02:24Z","timestamp":1784365344020,"version":"3.55.0"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:00:00Z","timestamp":1777939200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010418","name":"Institute of Information & Communications Technology Planning & Evaluation","doi-asserted-by":"publisher","award":["IITP-2026-RS-2023-00254177"],"award-info":[{"award-number":["IITP-2026-RS-2023-00254177"]}],"id":[{"id":"10.13039\/501100010418","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT, South Korea","doi-asserted-by":"publisher","award":["RS-2023-00245613"],"award-info":[{"award-number":["RS-2023-00245613"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT, South Korea","doi-asserted-by":"publisher","award":["RS-2024-00352439"],"award-info":[{"award-number":["RS-2024-00352439"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002701","name":"Korea Ministry of Education","doi-asserted-by":"publisher","award":["RS-2024-00346514"],"award-info":[{"award-number":["RS-2024-00346514"]}],"id":[{"id":"10.13039\/501100002701","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":[[2026,8]]},"DOI":"10.1016\/j.cagd.2026.102570","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:02:51Z","timestamp":1777993371000},"page":"102570","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Minimum distance computation for toroidal patch via topological classification"],"prefix":"10.1016","volume":"128","author":[{"given":"Minseok","family":"Kim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3893-5421","authenticated-orcid":false,"given":"Youngjin","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cagd.2026.102570_bib0005","series-title":"Proceedings. Computer Graphics International 2001","first-page":"215","article-title":"Ray tracing surfaces of revolution: an old problem with a new perspective","author":"Baciu","year":"2001"},{"key":"10.1016\/j.cagd.2026.102570_bib0010","series-title":"Eurographics 2018 (Short Papers)","first-page":"1","article-title":"Accelerating sphere tracing","author":"B\u00e1lint","year":"2018"},{"key":"10.1016\/j.cagd.2026.102570_bib0015","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1145\/358645.358661","article-title":"Strip trees: a hierarchical representation for curves","volume":"24","author":"Ballard","year":"1981","journal-title":"Commun. ACM"},{"key":"10.1016\/j.cagd.2026.102570_bib0020","series-title":"Eurographics 2023 (Short Papers)","first-page":"1","article-title":"Automatic step size relaxation in sphere tracing","author":"B\u00e1n","year":"2023"},{"key":"10.1016\/j.cagd.2026.102570_bib0025","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3450626.3459837","article-title":"Geometry and tool motion planning for curvature-adapted CNC machining","volume":"40","author":"Barton","year":"2021","journal-title":"ACM Trans. Graph."},{"key":"10.1016\/j.cagd.2026.102570_bib0030","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1016\/j.cag.2012.03.036","article-title":"A revisit to fitting parametric surfaces to point clouds","volume":"36","author":"Bo","year":"2012","journal-title":"Comput. Graph."},{"key":"10.1016\/j.cagd.2026.102570_bib0035","series-title":"Polygon Mesh Processing","author":"Botsch","year":"2010"},{"key":"10.1016\/j.cagd.2026.102570_bib0040","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1137\/0916069","article-title":"A limited memory algorithm for bound constrained optimization","volume":"16","author":"Byrd","year":"1995","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cagd.2026.102570_bib0045","article-title":"Collision-free tool motion planning for 5-axis CNC machining with toroidal cutters","volume":"173","author":"Chichell","year":"2024","journal-title":"Comput.-aided Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0050","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s10898-018-0645-y","article-title":"A simplicial homology algorithm for Lipschitz optimisation","volume":"72","author":"Endres","year":"2018","journal-title":"J. Glob. Optim."},{"key":"10.1016\/j.cagd.2026.102570_bib0055","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0167-8396(86)90005-1","article-title":"Surface algorithms using bounds on derivatives","volume":"3","author":"Filip","year":"1986","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0060","series-title":"Computer Graphics: Principles and Practice","volume":"vol. 12110","author":"Foley","year":"1996"},{"key":"10.1016\/j.cagd.2026.102570_bib0065","doi-asserted-by":"crossref","DOI":"10.1111\/cgf.13951","article-title":"Segment tracing using local Lipschitz bounds","author":"Galin","year":"2020","journal-title":"Comput. Graph. Forum"},{"key":"10.1016\/j.cagd.2026.102570_bib0070","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s003710050084","article-title":"Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces","volume":"12","author":"Hart","year":"1996","journal-title":"Vis. Comput."},{"key":"10.1016\/j.cagd.2026.102570_bib0075","series-title":"Fundamentals of Computer Aided Geometric Design","author":"Hoschek","year":"1993"},{"key":"10.1016\/j.cagd.2026.102570_bib0080","unstructured":"Jakob, W., Rhinelander, J., Moldovan, D., 2017. Version 3.0.0. Available at: Pybind11 \u2013 seamless operability between C++11 and Python. https:\/\/github.com\/pybind\/pybind11"},{"key":"10.1016\/j.cagd.2026.102570_bib0085","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s00371-004-0252-4","article-title":"Biconic subdivision of surfaces of revolution and its applications in intersection problems","volume":"20","author":"Jia","year":"2004","journal-title":"Vis. Comput."},{"key":"10.1016\/j.cagd.2026.102570_bib0090","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1145\/964967.801137","article-title":"New techniques for ray tracing procedurally defined objects","volume":"17","author":"Kajiya","year":"1983","journal-title":"ACM SIGGR. Comput. Graph."},{"key":"10.1016\/j.cagd.2026.102570_bib0095","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1145\/74334.74364","article-title":"Guaranteed ray intersections with implicit surfaces","volume":"23","author":"Kalra","year":"1989","journal-title":"ACM SIGGR. Comput. Graph."},{"key":"10.1016\/j.cagd.2026.102570_bib0100","series-title":"Smart Tools and Apps for Graphics - Eurographics Italian Chapter Conference","first-page":"1","article-title":"Enhanced sphere tracing","author":"Keinert","year":"2014"},{"key":"10.1016\/j.cagd.2026.102570_bib0105","article-title":"3d reconstruction of celadon from a 2d image: application to path tracing and VR","volume":"13","author":"Kim","year":"2023","journal-title":"Appl. Sci."},{"key":"10.1016\/j.cagd.2026.102570_bib0110","doi-asserted-by":"crossref","DOI":"10.1016\/j.jksuci.2023.101891","article-title":"A new spatial data structure for triangular mesh with toroidal patches","volume":"36","author":"Kim","year":"2024","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"10.1016\/j.cagd.2026.102570_bib0115","first-page":"116","article-title":"Orthogonal projection of points in CAD\/CAM applications: an overview","volume":"1","author":"Ko","year":"2014","journal-title":"J. Comput. Des. Eng."},{"key":"10.1016\/j.cagd.2026.102570_bib0120","series-title":"A Software Package for Sequential Quadratic Programming","author":"Kraft","year":"1988"},{"key":"10.1016\/j.cagd.2026.102570_bib0125","doi-asserted-by":"crossref","DOI":"10.1016\/j.cad.2025.103952","article-title":"On tool wear optimized motion planning for 5-axis CNC machining of free-form surfaces using toroidal cutting tools","volume":"189","author":"Kruppa","year":"2025","journal-title":"Comput.-aided Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0130","series-title":"Fast Proximity Queries with Swept Sphere Volumes","author":"Larsen","year":"1999"},{"key":"10.1016\/j.cagd.2026.102570_bib0135","doi-asserted-by":"crossref","first-page":"125","DOI":"10.4236\/jcc.2016.44011","article-title":"The analytical expressions for computing the minimum distance between a point and a torus","volume":"4","author":"Li","year":"2016","journal-title":"J. Comput. Commun."},{"key":"10.1016\/j.cagd.2026.102570_bib0140","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.cagd.2009.01.004","article-title":"A torus patch approximation approach for point projection on surfaces","volume":"26","author":"Liu","year":"2009","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0145","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1080\/10867651.1997.10487468","article-title":"Fast, minimum storage Ray-Triangle intersection","volume":"2","author":"M\u00f6ller","year":"1997","journal-title":"J. Graph. Tools"},{"key":"10.1016\/j.cagd.2026.102570_bib0150","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1137\/0721052","article-title":"Newton-type minimization via the Lanczos method","volume":"21","author":"Nash","year":"1984","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cagd.2026.102570_bib0155","series-title":"Numerical Optimization","author":"Nocedal","year":"2006"},{"key":"10.1016\/j.cagd.2026.102570_bib0160","doi-asserted-by":"crossref","DOI":"10.1016\/j.cad.2020.102866","article-title":"Surface\u2013surface-intersection computation using a bounding volume hierarchy with osculating toroidal patches in the leaf nodes","volume":"127","author":"Park","year":"2020","journal-title":"Comput.-aided Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0165","doi-asserted-by":"crossref","DOI":"10.1016\/j.cagd.2021.101979","article-title":"Self-intersection computation for freeform surfaces based on a regional representation scheme for miter points","volume":"86","author":"Park","year":"2021","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0170","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1778765.1778803","article-title":"Optix: a general purpose ray tracing engine","volume":"29","author":"Parker","year":"2010","journal-title":"ACM Trans. Graph."},{"key":"10.1016\/j.cagd.2026.102570_bib0175","author":"Quilez"},{"key":"10.1016\/j.cagd.2026.102570_bib0180","series-title":"Model-Based Derivative-Free Optimization Methods and Software","author":"Ragonneau","year":"2022"},{"key":"10.1016\/j.cagd.2026.102570_bib0185","unstructured":"Sawhney, R., 2021. Version 1.2.0. Available at: FCPW: fastest closest points in the west. https:\/\/github.com\/rohan-sawhney\/fcpw"},{"key":"10.1016\/j.cagd.2026.102570_bib0190","series-title":"Geometric Tools for Computer Graphics","author":"Schneider","year":"2002"},{"key":"10.1016\/j.cagd.2026.102570_bib0195","series-title":"Proceedings of the 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming","first-page":"11","article-title":"A performance analysis framework for identifying potential benefits in GPGPU applications","author":"Sim","year":"2012"},{"key":"10.1016\/j.cagd.2026.102570_bib0200","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1111\/cgf.13950","article-title":"Efficient minimum distance computation for solids of revolution","volume":"39","author":"Son","year":"2020","journal-title":"Comput. Graph. Forum"},{"key":"10.1016\/j.cagd.2026.102570_bib0205","doi-asserted-by":"crossref","DOI":"10.1016\/j.cagd.2021.101967","article-title":"Precise hausdorff distance computation for freeform surfaces based on computations with osculating toroidal patches","volume":"86","author":"Son","year":"2021","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.cagd.2026.102570_bib0210","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential evolution\u2013a simple and efficient heuristic for global optimization over continuous spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"10.1016\/j.cagd.2026.102570_bib0215","doi-asserted-by":"crossref","first-page":"2977","DOI":"10.1007\/s00170-025-16038-0","article-title":"Adaptive toolpath setup to reduce machining time when milling complex shape parts","volume":"139","author":"Vavruska","year":"2025","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"10.1016\/j.cagd.2026.102570_bib0220","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. Methods"},{"key":"10.1016\/j.cagd.2026.102570_bib0225","doi-asserted-by":"crossref","first-page":"5111","DOI":"10.1021\/jp970984n","article-title":"Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms","volume":"101","author":"Wales","year":"1997","journal-title":"J. Phys. Chem. A"},{"key":"10.1016\/j.cagd.2026.102570_bib0230","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1145\/1409625.1409626","article-title":"Parallel algorithms for approximation of distance maps on parametric surfaces","volume":"27","author":"Weber","year":"2008","journal-title":"ACM Trans. Graph."},{"key":"10.1016\/j.cagd.2026.102570_bib0235","doi-asserted-by":"crossref","DOI":"10.1145\/3543865","article-title":"High-Performance polynomial root finding for graphics","volume":"5","author":"Yuksel","year":"2022","journal-title":"Proc. ACM Comput. Graph. Interact. Tech."}],"container-title":["Computer Aided Geometric Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167839626000634?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167839626000634?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T08:02:28Z","timestamp":1784361748000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167839626000634"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":47,"alternative-id":["S0167839626000634"],"URL":"https:\/\/doi.org\/10.1016\/j.cagd.2026.102570","relation":{},"ISSN":["0167-8396"],"issn-type":[{"value":"0167-8396","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Minimum distance computation for toroidal patch via topological classification","name":"articletitle","label":"Article Title"},{"value":"Computer Aided Geometric Design","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cagd.2026.102570","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":"102570"}}