{"date_published":"1983-06-01T00:00:00Z","language":[{"iso":"eng"}],"issue":"4","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_created":"2018-12-11T12:07:06Z","quality_controlled":"1","extern":"1","abstract":[{"lang":"eng","text":"A generalization of the convex hull of a finite set of points in the plane is introduced and analyzed. This generalization leads to a family of straight-line graphs, \" \\alpha -shapes,\" which seem to capture the intuitive notions of \"fine shape\" and \"crude shape\" of point sets. It is shown that a-shapes are subgraphs of the closest point or furthest point Delaunay triangulation. Relying on this result an optimal O(n \\log n) algorithm that constructs \\alpha -shapes is developed."}],"date_updated":"2022-01-25T12:55:07Z","publication_status":"published","publisher":"IEEE","title":"On the shape of a set of points in the plane","intvolume":"        29","month":"06","article_type":"original","publication_identifier":{"eissn":["1558-0814"],"issn":["0018-9162"]},"oa_version":"None","year":"1983","acknowledgement":"The authors express their appreciation for numerous constructive suggestions, which led to improvements on\r\nvarious phases of the manuscript, to Dr. Marvin Simon of JPL and to Professor George L. Turin of University of\r\nCalifornia, Berkeley. The junior author also gratefully acknowledges the role of the latter as her M.S. research\r\nadvisor on the project which formed the nucleus of this work. \r\n","main_file_link":[{"url":"https://ieeexplore.ieee.org/document/1056714"}],"_id":"4128","day":"01","author":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"last_name":"Kirkpatrick","full_name":"Kirkpatrick, David","first_name":"David"},{"last_name":"Seidel","full_name":"Seidel, Raimund","first_name":"Raimund"}],"article_processing_charge":"No","doi":"10.1109/TIT.1983.1056714 ","publist_id":"1995","type":"journal_article","status":"public","citation":{"ieee":"H. Edelsbrunner, D. Kirkpatrick, and R. Seidel, “On the shape of a set of points in the plane,” <i>IEEE Transactions on Information Theory</i>, vol. 29, no. 4. IEEE, pp. 551–559, 1983.","mla":"Edelsbrunner, Herbert, et al. “On the Shape of a Set of Points in the Plane.” <i>IEEE Transactions on Information Theory</i>, vol. 29, no. 4, IEEE, 1983, pp. 551–59, doi:<a href=\"https://doi.org/10.1109/TIT.1983.1056714 \">10.1109/TIT.1983.1056714 </a>.","ama":"Edelsbrunner H, Kirkpatrick D, Seidel R. On the shape of a set of points in the plane. <i>IEEE Transactions on Information Theory</i>. 1983;29(4):551-559. doi:<a href=\"https://doi.org/10.1109/TIT.1983.1056714 \">10.1109/TIT.1983.1056714 </a>","ista":"Edelsbrunner H, Kirkpatrick D, Seidel R. 1983. On the shape of a set of points in the plane. IEEE Transactions on Information Theory. 29(4), 551–559.","apa":"Edelsbrunner, H., Kirkpatrick, D., &#38; Seidel, R. (1983). On the shape of a set of points in the plane. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.1983.1056714 \">https://doi.org/10.1109/TIT.1983.1056714 </a>","short":"H. Edelsbrunner, D. Kirkpatrick, R. Seidel, IEEE Transactions on Information Theory 29 (1983) 551–559.","chicago":"Edelsbrunner, Herbert, David Kirkpatrick, and Raimund Seidel. “On the Shape of a Set of Points in the Plane.” <i>IEEE Transactions on Information Theory</i>. IEEE, 1983. <a href=\"https://doi.org/10.1109/TIT.1983.1056714 \">https://doi.org/10.1109/TIT.1983.1056714 </a>."},"page":"551 - 559","publication":"IEEE Transactions on Information Theory","volume":29,"scopus_import":"1"}