{"language":[{"iso":"eng"}],"acknowledgement":"The author thanks Bei-Fang Chen, Siu-Wing Cheng, David Dobkin, Nikolai Dolbilin, Ping Fu, Sergei Ryshkov, and Vadim Shapiro for discussions on the topic of this paper.","extern":"1","publist_id":"2093","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"main_file_link":[{"url":"https://ieeexplore.ieee.org/abstract/document/492480"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"248 - 257","date_updated":"2022-06-13T12:27:11Z","publication":"Proceedings of IEEE 36th Annual Foundations of Computer Science","date_created":"2018-12-11T12:06:33Z","abstract":[{"lang":"eng","text":"Any arbitrary polyhedron P contained as a subset within Rd can be written as algebraic sum of simple terms, each an integer multiple of the intersection of d or fewer half-spaces defined by facets of P. P can be non-convex and can have holes of any kind. Among the consequences of this result are a short boolean formula for P, a fast parallel algorithm for point classification, and a new proof of the Gram-Sommerville angle relation."}],"status":"public","day":"01","year":"1995","date_published":"1995-10-01T00:00:00Z","quality_controlled":"1","article_processing_charge":"No","publication_identifier":{"issn":["0272-5428"]},"_id":"4034","month":"10","title":"Algebraic decomposition of non-convex polyhedra","oa_version":"None","citation":{"ieee":"H. Edelsbrunner, “Algebraic decomposition of non-convex polyhedra,” in <i>Proceedings of IEEE 36th Annual Foundations of Computer Science</i>, Milwaukee, WI, United States of America, 1995, pp. 248–257.","mla":"Edelsbrunner, Herbert. “Algebraic Decomposition of Non-Convex Polyhedra.” <i>Proceedings of IEEE 36th Annual Foundations of Computer Science</i>, IEEE, 1995, pp. 248–57.","chicago":"Edelsbrunner, Herbert. “Algebraic Decomposition of Non-Convex Polyhedra.” In <i>Proceedings of IEEE 36th Annual Foundations of Computer Science</i>, 248–57. IEEE, 1995.","ista":"Edelsbrunner H. 1995. Algebraic decomposition of non-convex polyhedra. Proceedings of IEEE 36th Annual Foundations of Computer Science. FOCS: Foundations of Computer Science, 248–257.","ama":"Edelsbrunner H. Algebraic decomposition of non-convex polyhedra. In: <i>Proceedings of IEEE 36th Annual Foundations of Computer Science</i>. IEEE; 1995:248-257.","apa":"Edelsbrunner, H. (1995). Algebraic decomposition of non-convex polyhedra. In <i>Proceedings of IEEE 36th Annual Foundations of Computer Science</i> (pp. 248–257). Milwaukee, WI, United States of America: IEEE.","short":"H. Edelsbrunner, in:, Proceedings of IEEE 36th Annual Foundations of Computer Science, IEEE, 1995, pp. 248–257."},"type":"conference","publisher":"IEEE","publication_status":"published","conference":{"name":"FOCS: Foundations of Computer Science","location":"Milwaukee, WI, United States of America","start_date":"1995-10-23","end_date":"1995-10-25"}}