{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T04:26:22Z","timestamp":1787372782546,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Traditional refinement algorithms insert a Steiner point from a few possible choices at each step. Our algorithm, on the contrary, defines regions from where a Steiner point can be selected and thus inserts a Steiner point among an infinite number of choices. Our algorithm significantly extends existing generalized algorithms by increasing the number and the size of these regions. The lower bound for newly created angles can be arbitrarily close to $30^{\\circ}$. Both termination and good grading are guaranteed. It is the first Delaunay refinement algorithm with a $30^{\\circ}$ angle bound and with grading guarantees. Experimental evaluation of our algorithm corroborates the theory.<\/jats:p>","DOI":"10.1137\/090763226","type":"journal-article","created":{"date-parts":[[2010,8,31]],"date-time":"2010-08-31T18:25:08Z","timestamp":1283279108000},"page":"2659-2686","source":"Crossref","is-referenced-by-count":14,"title":["Fully Generalized Two-Dimensional Constrained Delaunay Mesh Refinement"],"prefix":"10.1137","volume":"32","author":[{"given":"Panagiotis A.","family":"Foteinos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrey N.","family":"Chernikov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nikos P.","family":"Chrisochoides","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,8,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/24.2.162"},{"key":"R2","unstructured":"CGAL\n                      , Computational Geometry Algorithms Library\n                      , http:\/\/www.cgal.org."},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. N. Chernikov and N. P. Chrisochoides,\n                      Generalized Delaunay mesh refinement: From scalar to parallel\n                      , in Proceedings of the $15\\textrm{th}$ International Meshing Roundtable, P. P. P\u00e9bay, ed., Springer, Berlin, 2006, pp. 563\u2013580.","DOI":"10.1007\/978-3-540-34958-7_32"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"A. N. Chernikov and N. P. Chrisochoides,\n                      Three-dimensional semi-generalized point placement method for Delaunay mesh refinement\n                      , in Proceedings of the 16th International Meshing Roundtable, M. L. Brewer, D. Marcum, eds., Springer, Berlin, 2008, pp. 25\u201344.","DOI":"10.1007\/978-3-540-75103-8_2"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. N. Chernikov and N. P. 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