{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T02:27:07Z","timestamp":1648520827937},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1993,6]]},"abstract":"<jats:p> This paper presents a predictive solution to the problem of computing the intersections between a ray and a parametric polynomial surface patch. The method enhances the Bezier clipping technique which has emerged as an alternative to numerical and algebraic approaches. The improvement described here parallels the Aitken extrapolation used in accelerating convergence of numerical methods. We will first prove that, under certain conditions, the local parametric bounds in the Bezier clipping process are monotonically convergent over successive subdivisions. This implies that the de Casteljau step in each clipping tends to assume a certain pattern after sufficient subdivisions. Based on this observation, the global parametric estimate of an intersection is expressed as an infinite sum containing the local clip values. We then present a predictive scheme which achieves faster convergence than the original Bezier clipping technique. <\/jats:p>","DOI":"10.1142\/s0218195993000130","type":"journal-article","created":{"date-parts":[[2004,11,22]],"date-time":"2004-11-22T22:29:30Z","timestamp":1101162570000},"page":"203-219","source":"Crossref","is-referenced-by-count":0,"title":["A PREDICTIVE ALGORITHM FOR INTERSECTING PARAMETRIC POLYNOMIAL SURFACES"],"prefix":"10.1142","volume":"03","author":[{"given":"CLEMENT TAI-YIN","family":"SHIN","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Hong Kong, Pokfulam Road, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195993000130","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:57:43Z","timestamp":1565121463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195993000130"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":0,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,6]]}},"alternative-id":["10.1142\/S0218195993000130"],"URL":"https:\/\/doi.org\/10.1142\/s0218195993000130","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}