{"title":"Counting triangle crossings and halving planes","language":[{"iso":"eng"}],"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","author":[{"first_name":"Tamal","full_name":"Dey, Tamal","last_name":"Dey"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"}],"citation":{"ama":"Dey T, Edelsbrunner H. Counting triangle crossings and halving planes. <i>Discrete &#38; Computational Geometry</i>. 1994;12(1):281-289. doi:<a href=\"https://doi.org/10.1007/BF02574381\">10.1007/BF02574381</a>","apa":"Dey, T., &#38; Edelsbrunner, H. (1994). Counting triangle crossings and halving planes. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/BF02574381\">https://doi.org/10.1007/BF02574381</a>","chicago":"Dey, Tamal, and Herbert Edelsbrunner. “Counting Triangle Crossings and Halving Planes.” <i>Discrete &#38; Computational Geometry</i>. Springer, 1994. <a href=\"https://doi.org/10.1007/BF02574381\">https://doi.org/10.1007/BF02574381</a>.","ieee":"T. Dey and H. Edelsbrunner, “Counting triangle crossings and halving planes,” <i>Discrete &#38; Computational Geometry</i>, vol. 12, no. 1. Springer, pp. 281–289, 1994.","ista":"Dey T, Edelsbrunner H. 1994. Counting triangle crossings and halving planes. Discrete &#38; Computational Geometry. 12(1), 281–289.","short":"T. Dey, H. Edelsbrunner, Discrete &#38; Computational Geometry 12 (1994) 281–289.","mla":"Dey, Tamal, and Herbert Edelsbrunner. “Counting Triangle Crossings and Halving Planes.” <i>Discrete &#38; Computational Geometry</i>, vol. 12, no. 1, Springer, 1994, pp. 281–89, doi:<a href=\"https://doi.org/10.1007/BF02574381\">10.1007/BF02574381</a>."},"abstract":[{"lang":"eng","text":"Every collection of t≥2 n2 triangles with a total of n vertices in ℝ3 has Ω(t4/n6) crossing pairs. This implies that one of their edges meets Ω(t3/n6) of the triangles. From this it follows that n points in ℝ3 have only O(n8/3) halving planes."}],"volume":12,"acknowledgement":"The research of H. Edelsbrunner was supported by the National Science Foundation under Grant CCR-8921421 and under an Alan T. Waterman award, Grant CCR-9118874. Any opinions, findings and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the National Science Foundation.","status":"public","publication":"Discrete & Computational Geometry","publication_status":"published","issue":"1","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF02574381"}],"article_type":"original","intvolume":"        12","extern":"1","month":"09","article_processing_charge":"No","doi":"10.1007/BF02574381","publist_id":"2091","date_created":"2018-12-11T12:06:33Z","date_published":"1994-09-01T00:00:00Z","_id":"4032","publisher":"Springer","scopus_import":"1","quality_controlled":"1","oa_version":"None","date_updated":"2022-06-02T12:53:01Z","day":"01","type":"journal_article","year":"1994","publication_identifier":{"issn":["0179-5376"]},"page":"281 - 289"}