{"publication":"Proceedings of IEEE 36th Annual Foundations of Computer Science","publisher":"IEEE","type":"conference","status":"public","month":"10","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","conference":{"start_date":"1995-10-23","end_date":"1995-10-25","location":"Milwaukee, WI, United States of America","name":"FOCS: Foundations of Computer Science"},"day":"01","publist_id":"2093","quality_controlled":"1","page":"248 - 257","oa_version":"None","publication_status":"published","extern":"1","main_file_link":[{"url":"https://ieeexplore.ieee.org/abstract/document/492480"}],"author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","first_name":"Herbert"}],"citation":{"mla":"Edelsbrunner, Herbert. “Algebraic Decomposition of Non-Convex Polyhedra.” *Proceedings of IEEE 36th Annual Foundations of Computer Science*, IEEE, 1995, pp. 248–57.","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.","ieee":"H. Edelsbrunner, “Algebraic decomposition of non-convex polyhedra,” in *Proceedings of IEEE 36th Annual Foundations of Computer Science*, Milwaukee, WI, United States of America, 1995, pp. 248–257.","ama":"Edelsbrunner H. Algebraic decomposition of non-convex polyhedra. In: *Proceedings of IEEE 36th Annual Foundations of Computer Science*. IEEE; 1995:248-257.","short":"H. Edelsbrunner, in:, Proceedings of IEEE 36th Annual Foundations of Computer Science, IEEE, 1995, pp. 248–257.","apa":"Edelsbrunner, H. (1995). Algebraic decomposition of non-convex polyhedra. In *Proceedings of IEEE 36th Annual Foundations of Computer Science* (pp. 248–257). Milwaukee, WI, United States of America: IEEE.","chicago":"Edelsbrunner, Herbert. “Algebraic Decomposition of Non-Convex Polyhedra.” In *Proceedings of IEEE 36th Annual Foundations of Computer Science*, 248–57. IEEE, 1995."},"publication_identifier":{"issn":["0272-5428"]},"year":"1995","article_processing_charge":"No","title":"Algebraic decomposition of non-convex polyhedra","_id":"4034","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."}],"date_published":"1995-10-01T00:00:00Z","date_updated":"2022-06-13T12:27:11Z","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.","language":[{"iso":"eng"}]}