[{"main_file_link":[{"url":"https://dl.acm.org/doi/10.1145/174462.156635","open_access":"1"}],"oa":1,"quality_controlled":"1","doi":"10.1145/174462.156635","language":[{"iso":"eng"}],"month":"01","acknowledgement":"National Science Foundation under grant CCR-8921421 and Alan T. Waterman award, grant CCR-9118874.","year":"1994","publisher":"ACM","publication_status":"published","author":[{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert"},{"full_name":"Mücke, Ernst","first_name":"Ernst","last_name":"Mücke"}],"volume":13,"date_updated":"2022-06-02T12:00:42Z","date_created":"2018-12-11T12:06:34Z","publist_id":"2088","extern":"1","citation":{"chicago":"Edelsbrunner, Herbert, and Ernst Mücke. “Three-Dimensional Alpha Shapes.” ACM Transactions on Graphics. ACM, 1994. https://doi.org/10.1145/174462.156635.","mla":"Edelsbrunner, Herbert, and Ernst Mücke. “Three-Dimensional Alpha Shapes.” ACM Transactions on Graphics, vol. 13, no. 1, ACM, 1994, pp. 43–72, doi:10.1145/174462.156635.","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.","apa":"Edelsbrunner, H., & Mücke, E. (1994). Three-dimensional alpha shapes. ACM Transactions on Graphics. ACM. https://doi.org/10.1145/174462.156635","ieee":"H. Edelsbrunner and E. Mücke, “Three-dimensional alpha shapes,” ACM Transactions on Graphics, vol. 13, no. 1. ACM, pp. 43–72, 1994.","ama":"Edelsbrunner H, Mücke E. Three-dimensional alpha shapes. ACM Transactions on Graphics. 1994;13(1):43-72. doi:10.1145/174462.156635"},"publication":"ACM Transactions on Graphics","page":"43 - 72","date_published":"1994-01-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01","_id":"4037","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","intvolume":" 13","status":"public","title":"Three-dimensional alpha shapes","oa_version":"None","type":"journal_article","issue":"1","abstract":[{"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.","lang":"eng"}]}]