{"oa_version":"None","publist_id":"2088","type":"journal_article","page":"43 - 72","year":"1994","author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Ernst","last_name":"Mücke","full_name":"Mücke, Ernst"}],"doi":"10.1145/174462.156635","issue":"1","abstract":[{"lang":"eng","text":"Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the `'shape” of the set. For that purpose, this article introduces the formal notion of the family of alpha-shapes of a finite point set in R3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter alpha is-an-element-of R controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size n in time O(n2), worst case. A robust implementation of the algorithm is discussed, and several applications in the area of scientific computing are mentioned."}],"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://dl.acm.org/doi/10.1145/174462.156635"}],"publication":"ACM Transactions on Graphics","extern":"1","scopus_import":"1","date_updated":"2022-06-02T12:00:42Z","article_processing_charge":"No","intvolume":"        13","citation":{"chicago":"Edelsbrunner, Herbert, and Ernst Mücke. “Three-Dimensional Alpha Shapes.” <i>ACM Transactions on Graphics</i>. ACM, 1994. <a href=\"https://doi.org/10.1145/174462.156635\">https://doi.org/10.1145/174462.156635</a>.","apa":"Edelsbrunner, H., &#38; Mücke, E. (1994). Three-dimensional alpha shapes. <i>ACM Transactions on Graphics</i>. ACM. <a href=\"https://doi.org/10.1145/174462.156635\">https://doi.org/10.1145/174462.156635</a>","short":"H. Edelsbrunner, E. Mücke, ACM Transactions on Graphics 13 (1994) 43–72.","ista":"Edelsbrunner H, Mücke E. 1994. Three-dimensional alpha shapes. ACM Transactions on Graphics. 13(1), 43–72.","mla":"Edelsbrunner, Herbert, and Ernst Mücke. “Three-Dimensional Alpha Shapes.” <i>ACM Transactions on Graphics</i>, vol. 13, no. 1, ACM, 1994, pp. 43–72, doi:<a href=\"https://doi.org/10.1145/174462.156635\">10.1145/174462.156635</a>.","ieee":"H. Edelsbrunner and E. Mücke, “Three-dimensional alpha shapes,” <i>ACM Transactions on Graphics</i>, vol. 13, no. 1. ACM, pp. 43–72, 1994.","ama":"Edelsbrunner H, Mücke E. Three-dimensional alpha shapes. <i>ACM Transactions on Graphics</i>. 1994;13(1):43-72. doi:<a href=\"https://doi.org/10.1145/174462.156635\">10.1145/174462.156635</a>"},"title":"Three-dimensional alpha shapes","publisher":"ACM","month":"01","oa":1,"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","acknowledgement":"National Science Foundation under grant CCR-8921421 and  Alan T. Waterman award, grant CCR-9118874.","volume":13,"publication_status":"published","_id":"4037","day":"01","date_published":"1994-01-01T00:00:00Z","status":"public","date_created":"2018-12-11T12:06:34Z","quality_controlled":"1"}