{"volume":12,"article_type":"original","quality_controlled":"1","day":"01","abstract":[{"lang":"eng","text":"A general and direct method for computing the Betti numbers of a finite simplicial complex in Bd is given. This method is complete for d less than or equal to 3, where versions of this method run in time O(n alpha(n)) and O(n), n the number of simplices. An implementation of the algorithm is applied to alpha shapes, which is a novel geometric modeling tool."}],"status":"public","intvolume":"        12","date_updated":"2022-06-24T09:49:32Z","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/016783969500016Y?via%3Dihub"}],"extern":"1","acknowledgement":"This work is supported by the National Science Foundation under grant ASC-9200301 and the Alan T. Waterman award, grant CCR-9118874. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the National Science Foundation.","publication_status":"published","publisher":"Elsevier","scopus_import":"1","citation":{"mla":"Delfinado, Cecil, and Herbert Edelsbrunner. “An Incremental Algorithm for Betti Numbers of Simplicial Complexes on the 3-Sphere.” <i>Computer Aided Geometric Design</i>, vol. 12, no. 7, Elsevier, 1995, pp. 771–84, doi:<a href=\"https://doi.org/10.1016/0167-8396(95)00016-Y\">10.1016/0167-8396(95)00016-Y</a>.","ieee":"C. Delfinado and H. Edelsbrunner, “An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere,” <i>Computer Aided Geometric Design</i>, vol. 12, no. 7. Elsevier, pp. 771–784, 1995.","chicago":"Delfinado, Cecil, and Herbert Edelsbrunner. “An Incremental Algorithm for Betti Numbers of Simplicial Complexes on the 3-Sphere.” <i>Computer Aided Geometric Design</i>. Elsevier, 1995. <a href=\"https://doi.org/10.1016/0167-8396(95)00016-Y\">https://doi.org/10.1016/0167-8396(95)00016-Y</a>.","ista":"Delfinado C, Edelsbrunner H. 1995. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Computer Aided Geometric Design. 12(7), 771–784.","ama":"Delfinado C, Edelsbrunner H. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. <i>Computer Aided Geometric Design</i>. 1995;12(7):771-784. doi:<a href=\"https://doi.org/10.1016/0167-8396(95)00016-Y\">10.1016/0167-8396(95)00016-Y</a>","apa":"Delfinado, C., &#38; Edelsbrunner, H. (1995). An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. <i>Computer Aided Geometric Design</i>. Elsevier. <a href=\"https://doi.org/10.1016/0167-8396(95)00016-Y\">https://doi.org/10.1016/0167-8396(95)00016-Y</a>","short":"C. Delfinado, H. Edelsbrunner, Computer Aided Geometric Design 12 (1995) 771–784."},"type":"journal_article","oa_version":"None","month":"11","issue":"7","title":"An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere","_id":"4029","publication_identifier":{"issn":["0167-8396"]},"doi":"10.1016/0167-8396(95)00016-Y","article_processing_charge":"No","date_published":"1995-11-01T00:00:00Z","year":"1995","date_created":"2018-12-11T12:06:32Z","publication":"Computer Aided Geometric Design","page":"771 - 784","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"last_name":"Delfinado","first_name":"Cecil","full_name":"Delfinado, Cecil"},{"full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"2096","language":[{"iso":"eng"}]}