[{"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.","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","issue":"7","intvolume":"        12","volume":12,"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/016783969500016Y?via%3Dihub"}],"scopus_import":"1","extern":"1","date_published":"1995-11-01T00:00:00Z","article_processing_charge":"No","month":"11","title":"An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere","date_updated":"2022-06-24T09:49:32Z","date_created":"2018-12-11T12:06:32Z","_id":"4029","page":"771 - 784","publication":"Computer Aided Geometric Design","quality_controlled":"1","language":[{"iso":"eng"}],"status":"public","abstract":[{"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.","lang":"eng"}],"publication_status":"published","publist_id":"2096","article_type":"original","type":"journal_article","citation":{"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>.","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>","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>.","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.","short":"C. Delfinado, H. Edelsbrunner, Computer Aided Geometric Design 12 (1995) 771–784.","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>","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."},"author":[{"first_name":"Cecil","full_name":"Delfinado, Cecil","last_name":"Delfinado"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"}],"year":"1995","publication_identifier":{"issn":["0167-8396"]},"day":"01","publisher":"Elsevier","oa_version":"None","doi":"10.1016/0167-8396(95)00016-Y"}]