{"abstract":[{"text":"The main result of this paper is an extension of de Silva's Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset of the i + 1 points has a weak witness.","lang":"eng"}],"author":[{"first_name":"Dominique","last_name":"Attali","full_name":"Attali, Dominique"},{"first_name":"Herbert","full_name":"Herbert Edelsbrunner","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Yuriy","full_name":"Mileyko, Yuriy","last_name":"Mileyko"}],"status":"public","main_file_link":[{"open_access":"1","url":"https://hal.archives-ouvertes.fr/hal-00201055"}],"year":"2007","_id":"3561","publication_status":"published","page":"143 - 150","date_published":"2007-06-01T00:00:00Z","publisher":"ACM","publist_id":"2824","type":"conference","oa":1,"date_created":"2018-12-11T12:03:58Z","title":"Weak witnesses for Delaunay triangulations of submanifolds","date_updated":"2021-01-12T07:44:19Z","month":"06","doi":"10.1145/1236246.1236267","day":"01","quality_controlled":0,"citation":{"short":"D. Attali, H. Edelsbrunner, Y. Mileyko, in:, ACM, 2007, pp. 143–150.","ama":"Attali D, Edelsbrunner H, Mileyko Y. Weak witnesses for Delaunay triangulations of submanifolds. In: ACM; 2007:143-150. doi:<a href=\"https://doi.org/10.1145/1236246.1236267\">10.1145/1236246.1236267</a>","ieee":"D. Attali, H. Edelsbrunner, and Y. Mileyko, “Weak witnesses for Delaunay triangulations of submanifolds,” presented at the SPM: Symposium on Solid and Physical Modeling, 2007, pp. 143–150.","apa":"Attali, D., Edelsbrunner, H., &#38; Mileyko, Y. (2007). Weak witnesses for Delaunay triangulations of submanifolds (pp. 143–150). Presented at the SPM: Symposium on Solid and Physical Modeling, ACM. <a href=\"https://doi.org/10.1145/1236246.1236267\">https://doi.org/10.1145/1236246.1236267</a>","chicago":"Attali, Dominique, Herbert Edelsbrunner, and Yuriy Mileyko. “Weak Witnesses for Delaunay Triangulations of Submanifolds,” 143–50. ACM, 2007. <a href=\"https://doi.org/10.1145/1236246.1236267\">https://doi.org/10.1145/1236246.1236267</a>.","mla":"Attali, Dominique, et al. <i>Weak Witnesses for Delaunay Triangulations of Submanifolds</i>. ACM, 2007, pp. 143–50, doi:<a href=\"https://doi.org/10.1145/1236246.1236267\">10.1145/1236246.1236267</a>.","ista":"Attali D, Edelsbrunner H, Mileyko Y. 2007. Weak witnesses for Delaunay triangulations of submanifolds. SPM: Symposium on Solid and Physical Modeling, 143–150."},"extern":1,"conference":{"name":"SPM: Symposium on Solid and Physical Modeling"}}