{"publist_id":"2090","language":[{"iso":"eng"}],"intvolume":"        12","quality_controlled":"1","scopus_import":"1","title":"Ray shooting in polygons using geodesic triangulations","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01377183"}],"oa_version":"None","issue":"1","day":"01","article_type":"original","year":"1994","publisher":"Springer","date_published":"1994-07-01T00:00:00Z","extern":"1","type":"journal_article","date_updated":"2022-06-02T12:41:07Z","volume":12,"publication_identifier":{"issn":["0178-4617"]},"_id":"4039","doi":"10.1007/BF01377183","author":[{"last_name":"Chazelle","first_name":"Bernard","full_name":"Chazelle, Bernard"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"full_name":"Grigni, Michelangelo","first_name":"Michelangelo","last_name":"Grigni"},{"full_name":"Guibas, Leonidas","first_name":"Leonidas","last_name":"Guibas"},{"first_name":"John","full_name":"Hershberger, John","last_name":"Hershberger"},{"last_name":"Sharir","first_name":"Micha","full_name":"Sharir, Micha"},{"last_name":"Snoeyink","first_name":"Jack","full_name":"Snoeyink, Jack"}],"abstract":[{"lang":"eng","text":"Let P be a simple polygon with n vertices. We present a simple decomposition scheme that partitions the interior of P into O(n) so-called geodesic triangles, so that any line segment interior to P crosses at most 2 log n of these triangles. This decomposition can be used to preprocess P in a very simple manner, so that any ray-shooting query can be answered in time O(log n). The data structure requires O(n) storage and O(n log n) preprocessing time. By using more sophisticated techniques, we can reduce the preprocessing time to O(n). We also extend our general technique to the case of ray shooting amidst k polygonal obstacles with a total of n edges, so that a query can be answered in O(√ log n) time."}],"publication_status":"published","publication":"Algorithmica","acknowledgement":"Work by Bernard Chazelle has been supported by NSF Grant CCR-87-00917. Work by Herbert Edelsbrunner has been supported by NSF Grant CCR-89-21421. Work by Micha Sharir has been supported by ONR Grants N00014-89-J-3042 and N00014-90-J-1284, by NSF Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.","article_processing_charge":"No","month":"07","date_created":"2018-12-11T12:06:35Z","citation":{"chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Michelangelo Grigni, Leonidas Guibas, John Hershberger, Micha Sharir, and Jack Snoeyink. “Ray Shooting in Polygons Using Geodesic Triangulations.” <i>Algorithmica</i>. Springer, 1994. <a href=\"https://doi.org/10.1007/BF01377183\">https://doi.org/10.1007/BF01377183</a>.","ista":"Chazelle B, Edelsbrunner H, Grigni M, Guibas L, Hershberger J, Sharir M, Snoeyink J. 1994. Ray shooting in polygons using geodesic triangulations. Algorithmica. 12(1), 54–68.","apa":"Chazelle, B., Edelsbrunner, H., Grigni, M., Guibas, L., Hershberger, J., Sharir, M., &#38; Snoeyink, J. (1994). Ray shooting in polygons using geodesic triangulations. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01377183\">https://doi.org/10.1007/BF01377183</a>","short":"B. Chazelle, H. Edelsbrunner, M. Grigni, L. Guibas, J. Hershberger, M. Sharir, J. Snoeyink, Algorithmica 12 (1994) 54–68.","mla":"Chazelle, Bernard, et al. “Ray Shooting in Polygons Using Geodesic Triangulations.” <i>Algorithmica</i>, vol. 12, no. 1, Springer, 1994, pp. 54–68, doi:<a href=\"https://doi.org/10.1007/BF01377183\">10.1007/BF01377183</a>.","ama":"Chazelle B, Edelsbrunner H, Grigni M, et al. Ray shooting in polygons using geodesic triangulations. <i>Algorithmica</i>. 1994;12(1):54-68. doi:<a href=\"https://doi.org/10.1007/BF01377183\">10.1007/BF01377183</a>","ieee":"B. Chazelle <i>et al.</i>, “Ray shooting in polygons using geodesic triangulations,” <i>Algorithmica</i>, vol. 12, no. 1. Springer, pp. 54–68, 1994."},"status":"public","page":"54 - 68","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17"}