{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:08:12Z","timestamp":1761808092609},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Methods to estimate surface areas of geometric objects in\n3D are well known. A number of these methods are of Monte Carlo type,\nand some are based on the Cauchy\u2013Crofton formula from integral geometry.\nEmploying this formula requires the generation of sets of random lines that\nare uniformly distributed in 3D. One model to generate sets of random lines\nthat are uniformly distributed in 3D is called the tangent model (see\n[4]). In this paper, we present an extension of this model to\nhigher dimensions, and we examine its performance by estimating hypersurface\nareas of <jats:italic>n<\/jats:italic>-ellipsoids. Then we apply this method to estimate surface areas\nof hypersurfaces defined by Fermat-type varieties of even degree.<\/jats:p>","DOI":"10.1515\/mcma-2017-0100","type":"journal-article","created":{"date-parts":[[2017,1,28]],"date-time":"2017-01-28T18:15:56Z","timestamp":1485627356000},"page":"13-20","source":"Crossref","is-referenced-by-count":6,"title":["On the tangent model for the density of lines and a Monte Carlo method for computing hypersurface area"],"prefix":"10.1515","volume":"23","author":[{"given":"Khaldoun","family":"El Khaldi","sequence":"first","affiliation":[{"name":"Department of Computer Science, Notre Dame University-Louaize, Zouk Mosbeh, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elias G.","family":"Saleeby","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Natural Science, American University of Iraq,Sulaimani, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,1,28]]},"reference":[{"key":"2023040100373530857_j_mcma-2017-0100_ref_001_w2aab2b8d443b1b7b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Beckers A. L. D. and Smeulders A. W. M.,\nThe probability of a random straight line in two and three dimensions,\nPattern Recognit. Let. 11 (1990), 233\u2013240.","DOI":"10.1016\/0167-8655(90)90061-6"},{"key":"2023040100373530857_j_mcma-2017-0100_ref_002_w2aab2b8d443b1b7b1ab2b1b2Aa","unstructured":"El Khaldi K. and Saleeby E. G.,\nPerimeters of fermat ovals,\nMath. Sci. 41 (2016), no. 1, 53\u201360."},{"key":"2023040100373530857_j_mcma-2017-0100_ref_003_w2aab2b8d443b1b7b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"Hyksova M., Kalousova A. and Saxl I.,\nEarly history of geometric probability and stereology,\nImage Anal. Stereol. 31 (2012), 1\u201316.","DOI":"10.5566\/ias.v31.p1-16"},{"key":"2023040100373530857_j_mcma-2017-0100_ref_004_w2aab2b8d443b1b7b1ab2b1b4Aa","doi-asserted-by":"crossref","unstructured":"Li X., Wang W., Martin R. R. and Bowyer A.,\nUsing low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models,\nComput. Aided Geom. 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A.,\nIntegral Geometry and Geometric Probability, 2nd ed.,\nCambridge University Press, Cambridge, 2004."},{"key":"2023040100373530857_j_mcma-2017-0100_ref_008_w2aab2b8d443b1b7b1ab2b1b8Aa","doi-asserted-by":"crossref","unstructured":"Sibuya M.,\nA method for generating uniformly distributed points on N-dimensional spheres,\nAnn. Inst. Statist. Math. 14 (1964), 81\u201385.","DOI":"10.1007\/BF02868626"},{"key":"2023040100373530857_j_mcma-2017-0100_ref_009_w2aab2b8d443b1b7b1ab2b1b9Aa","unstructured":"Solomon H.,\nGeometric Probability,\nSIAM, Philadelphia, 1985."},{"key":"2023040100373530857_j_mcma-2017-0100_ref_010_w2aab2b8d443b1b7b1ab2b1c10Aa","doi-asserted-by":"crossref","unstructured":"Tashiro Y.,\nOn methods for generating uniform random points on the surface of a sphere,\nAnn. Inst. Statist. Math. 29 (1977), 295\u2013300.","DOI":"10.1007\/BF02532791"},{"key":"2023040100373530857_j_mcma-2017-0100_ref_011_w2aab2b8d443b1b7b1ab2b1c11Aa","unstructured":"Tee G. J.,\nSurface area and capacity of ellipsoids in n dimension,\nNew Zealand J. Math. 34 (2005), 165\u2013198."}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/mcma.2017.23.issue-1\/mcma-2017-0100\/mcma-2017-0100.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2017-0100\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2017-0100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T15:57:56Z","timestamp":1680364676000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2017-0100\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,28]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,2,21]]},"published-print":{"date-parts":[[2017,3,1]]}},"alternative-id":["10.1515\/mcma-2017-0100"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2017-0100","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,28]]}}}