{"day":"01","acknowledgement":"The research of the second author is partially supported by NSF under grant DBI-0820624 and by DARPA under grants HR011-05-1-0057 and HR0011-09-006\r\n","page":"507 - 519","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","department":[{"_id":"HeEd"}],"publication":"Computational Geometry","publisher":"Elsevier","author":[{"first_name":"Thanhtung","last_name":"Cao","full_name":"Cao, Thanhtung"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert"},{"first_name":"Tiowseng","last_name":"Tan","full_name":"Tan, Tiowseng"}],"abstract":[{"lang":"eng","text":"We prove that the dual of the digital Voronoi diagram constructed by flooding the plane from the data points gives a geometrically and topologically correct dual triangulation. This provides the proof of correctness for recently developed GPU algorithms that outperform traditional CPU algorithms for constructing two-dimensional Delaunay triangulations."}],"status":"public","_id":"1578","quality_controlled":"1","oa_version":"None","scopus_import":1,"publist_id":"5593","citation":{"apa":"Cao, T., Edelsbrunner, H., &#38; Tan, T. (2015). Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>","mla":"Cao, Thanhtung, et al. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” <i>Computational Geometry</i>, vol. 48, no. 7, Elsevier, 2015, pp. 507–19, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>.","ista":"Cao T, Edelsbrunner H, Tan T. 2015. Triangulations from topologically correct digital Voronoi diagrams. Computational Geometry. 48(7), 507–519.","short":"T. Cao, H. Edelsbrunner, T. Tan, Computational Geometry 48 (2015) 507–519.","ama":"Cao T, Edelsbrunner H, Tan T. Triangulations from topologically correct digital Voronoi diagrams. <i>Computational Geometry</i>. 2015;48(7):507-519. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">10.1016/j.comgeo.2015.04.001</a>","ieee":"T. Cao, H. Edelsbrunner, and T. Tan, “Triangulations from topologically correct digital Voronoi diagrams,” <i>Computational Geometry</i>, vol. 48, no. 7. Elsevier, pp. 507–519, 2015.","chicago":"Cao, Thanhtung, Herbert Edelsbrunner, and Tiowseng Tan. “Triangulations from Topologically Correct Digital Voronoi Diagrams.” <i>Computational Geometry</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2015.04.001\">https://doi.org/10.1016/j.comgeo.2015.04.001</a>."},"doi":"10.1016/j.comgeo.2015.04.001","month":"08","publication_status":"published","date_published":"2015-08-01T00:00:00Z","intvolume":"        48","date_created":"2018-12-11T11:52:49Z","date_updated":"2021-01-12T06:51:43Z","issue":"7","language":[{"iso":"eng"}],"title":"Triangulations from topologically correct digital Voronoi diagrams","year":"2015","volume":48}