{"abstract":[{"lang":"eng","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."}],"publication_status":"published","title":"Weak witnesses for Delaunay triangulations of submanifolds","quality_controlled":0,"conference":{"name":"SPM: Symposium on Solid and Physical Modeling"},"doi":"10.1145/1236246.1236267","author":[{"full_name":"Attali, Dominique","first_name":"Dominique","last_name":"Attali"},{"orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Herbert Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"last_name":"Mileyko","first_name":"Yuriy","full_name":"Mileyko, Yuriy"}],"_id":"3561","main_file_link":[{"open_access":"1","url":"https://hal.archives-ouvertes.fr/hal-00201055"}],"type":"conference","extern":1,"date_updated":"2021-01-12T07:44:19Z","publist_id":"2824","oa":1,"date_published":"2007-06-01T00:00:00Z","day":"01","page":"143 - 150","status":"public","publisher":"ACM","year":"2007","date_created":"2018-12-11T12:03:58Z","month":"06","citation":{"short":"D. Attali, H. Edelsbrunner, Y. Mileyko, in:, ACM, 2007, pp. 143–150.","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>.","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.","ista":"Attali D, Edelsbrunner H, Mileyko Y. 2007. Weak witnesses for Delaunay triangulations of submanifolds. SPM: Symposium on Solid and Physical Modeling, 143–150.","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>.","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>"}}