{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T21:10:46Z","timestamp":1723237846171},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2014,12,5]],"date-time":"2014-12-05T00:00:00Z","timestamp":1417737600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Vis Comput"],"published-print":{"date-parts":[[2015,11]]},"DOI":"10.1007\/s00371-014-1028-0","type":"journal-article","created":{"date-parts":[[2014,12,4]],"date-time":"2014-12-04T12:54:04Z","timestamp":1417697644000},"page":"1487-1500","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Computation of point inversion and ray-surface intersection through tracing along the base surface"],"prefix":"10.1007","volume":"31","author":[{"given":"Xiaoping","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weizhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,12,5]]},"reference":[{"issue":"1","key":"1028_CR1","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/MCG.1986.276742","volume":"6","author":"TW Sederberg","year":"1986","unstructured":"Sederberg, T.W.: Algebraic geometry for computer aided geometric design. IEEE Comput. Graph. Appl. 6(1), 52\u201359 (1986)","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"Ser. 2","key":"1028_CR2","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1112\/plms\/s2-6.1.468","volume":"6","author":"AL Dixon","year":"1908","unstructured":"Dixon, A.L.: The eliminant of three quantics in two independent variables. Proc. Lond. Math. Soc. 6(Ser. 2), 468\u2013478 (1908)","journal-title":"Proc. Lond. Math. Soc."},{"issue":"1","key":"1028_CR3","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/38.180121","volume":"13","author":"CM Hoffmann","year":"1993","unstructured":"Hoffmann, C.M.: Implicit curves and surfaces in CAGD. IEEE Comput. Graph. Appl. 13(1), 79\u201388 (1993)","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"1","key":"1028_CR4","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/0734-189X(84)90140-3","volume":"28","author":"TW Sederberg","year":"1984","unstructured":"Sederberg, T.W., Anderson, D.C., Goldman, R.N.: Implicit representation of parametric curves and surfaces. Comput. Vis. Graph. Image Process. 28(1), 72\u201384 (1984)","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"1028_CR5","volume-title":"Handbook of computer aided geometric design","author":"G Farin","year":"2002","unstructured":"Farin, G., Hoschek, J., Kim, M.S.: Handbook of computer aided geometric design. North Holland, Amsterdam (2002)"},{"key":"1028_CR6","volume-title":"Fundamentals of computer aided geometric design","author":"J Hoschek","year":"1993","unstructured":"Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. A K Peters, Wellesley (1993)"},{"issue":"5","key":"1028_CR7","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0167-8396(99)00003-5","volume":"16","author":"E Hartmann","year":"1999","unstructured":"Hartmann, E.: On the curvature of curves and surfaces defined by normalforms. Comput. Aided Geom. Design 16(5), 355\u2013376 (1999)","journal-title":"Comput. Aided Geom. Design"},{"issue":"3","key":"1028_CR8","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.cagd.2004.12.001","volume":"22","author":"SM Hu","year":"2005","unstructured":"Hu, S.M., Wallner, J.: A second order algorithm for orthogonal projection onto curves and surfaces. Comput. Aided Geom. Design 22(3), 251\u2013260 (2005)","journal-title":"Comput. Aided Geom. Design"},{"issue":"5","key":"1028_CR9","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.cagd.2009.01.004","volume":"26","author":"XM Liu","year":"2009","unstructured":"Liu, X.M., Yang, L., Yong, J.H., Gu, H.J., Sun, J.G.: A torus patch approximation approach for point projection on surfaces. Comput. Aided Geom. Design 26(5), 593\u2013598 (2009)","journal-title":"Comput. Aided Geom. Design"},{"issue":"8","key":"1028_CR10","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/S0010-4485(00)00103-2","volume":"33","author":"LA Piegl","year":"2001","unstructured":"Piegl, L.A., Tiller, W.: Parameterization for surface fitting in reverse engineering. Comput. Aided Design 33(8), 593\u2013603 (2001)","journal-title":"Comput. Aided Design"},{"issue":"2","key":"1028_CR11","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0167-8396(03)00021-9","volume":"20","author":"YL Ma","year":"2003","unstructured":"Ma, Y.L., Hewitt, W.T.: Point inversion and projection for NURBS curve and surface: control polygon approach. Comput. Aided Geom. Design 20(2), 79\u201399 (2003)","journal-title":"Comput. Aided Geom. Design"},{"key":"1028_CR12","unstructured":"The Math Works Inc.: Using MATLAB, Version 6. The Math Works Inc., Natick (2000)"},{"issue":"4","key":"1028_CR13","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1080\/10867651.1999.10487513","volume":"4","author":"J Hughes","year":"1999","unstructured":"Hughes, J., M\u00f6ller, T.: Building an orthonormal basis from a unit vector. J. Graph. Tools 4(4), 33\u201335 (1999)","journal-title":"J. Graph. Tools"},{"issue":"3","key":"1028_CR14","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1145\/965145.801287","volume":"16","author":"JT Kajiya","year":"1982","unstructured":"Kajiya, J.T.: Ray tracing parametric patches. Comput. Graph. 16(3), 245\u2013254 (1982)","journal-title":"Comput. Graph."},{"issue":"3","key":"1028_CR15","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1145\/325165.325233","volume":"19","author":"DL Toth","year":"1985","unstructured":"Toth, D.L.: On ray tracing parametric surfaces. Comput. Graph. 19(3), 171\u2013179 (1985)","journal-title":"Comput. Graph."},{"issue":"5","key":"1028_CR16","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/S0097-8493(97)87263-9","volume":"21","author":"Q Kaihuai","year":"1997","unstructured":"Kaihuai, Q., Minglun, G., Youjiang, G., Wenping, W.: A new method for speeding up ray tracing NURBS surfaces. Comput. Graph. 21(5), 577\u2013586 (1997)","journal-title":"Comput. Graph."},{"issue":"2","key":"1028_CR17","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1109\/TVCG.2009.41","volume":"16","author":"JM Singh","year":"2010","unstructured":"Singh, J.M., Narayanan, P.J.: Real-time ray-tracing of implicit surfaces on the GPU. IEEE Trans. Vis. Comput. Graph. 16(2), 261\u2013272 (2010)","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"1028_CR18","doi-asserted-by":"crossref","unstructured":"Abert, O., Geimer, M., M\u00fcller, S.: Direct and fast ray tracing of NURBS surfaces. In: Proceedings of the 2006 IEEE Symposium on Interactive Ray Tracing, Salt Lake, September 18\u201320 (2006)","DOI":"10.1109\/RT.2006.280227"},{"key":"1028_CR19","volume-title":"Numerical Recipes in C, the art of Scientific Computing","author":"WH Press","year":"1999","unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C, the art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1999)","edition":"2"},{"key":"1028_CR20","doi-asserted-by":"crossref","unstructured":"Petcu, D.: Numerical solution of ODEs with distributed maple. Lecture Notes in Computer Science 1988, 341\u2013357 (2001)","DOI":"10.1007\/3-540-45262-1_79"},{"key":"1028_CR21","unstructured":"Hairer, E., N\u00f8rsett, S.P., Wanner, G.: Solving ordinary differential equations I, non-stiff problems. 2nd ed. Springer, New York (1993)"},{"key":"1028_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05221-7","volume-title":"Solving ordinary differential equations II, stiff and differential-algebraic problems","author":"E Hairer","year":"1996","unstructured":"Hairer, E., Wanner, G.: Solving ordinary differential equations II, stiff and differential-algebraic problems, 2nd edn. Springer, New York (1996)","edition":"2"},{"key":"1028_CR23","volume-title":"Geometric numerical integration structure-preserving algorithms for ordinary differential equations","author":"E Hairer","year":"2002","unstructured":"Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration structure-preserving algorithms for ordinary differential equations. Springer, New York (2002)"},{"key":"1028_CR24","first-page":"541","volume":"18","author":"S Wang","year":"2001","unstructured":"Wang, S., Shih, Z., Chang, R.: An efficient and stable ray tracing algorithm for parametric surfaces. J. Inf. Sci. Eng. 18, 541\u2013561 (2001)","journal-title":"J. Inf. Sci. Eng."},{"issue":"4","key":"1028_CR25","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1007\/s11704-009-0034-2","volume":"3","author":"J-T Xu","year":"2009","unstructured":"Xu, J.-T., Liu, W.-J., Wu, J.-H., Bian, H.-Y., Li, L.: Geometric algorithm for point projection and inversion onto B\u00e9zier surfaces. Front. Comput. Sci. China 3(4), 472\u2013476 (2009)","journal-title":"Front. Comput. Sci. China"},{"key":"1028_CR26","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/j.cagd.2013.07.001","volume":"308","author":"T Park","year":"2013","unstructured":"Park, T., Ji, J., Ko, K.H.: A second order geometric method for ray\/parametric surface intersection. Comput. Aided Geom. Design 308, 795\u2013804 (2013)","journal-title":"Comput. Aided Geom. Design"},{"key":"1028_CR27","doi-asserted-by":"crossref","unstructured":"Pegna, J.; Wolter, F.E.: Surface curve design by orthogonal projection of space curves onto free-form surfaces. J. Mech. Design 118(1), 45\u201352 (1996)","DOI":"10.1115\/1.2826855"}],"container-title":["The Visual Computer"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00371-014-1028-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00371-014-1028-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00371-014-1028-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T14:59:38Z","timestamp":1559055578000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00371-014-1028-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,5]]},"references-count":27,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2015,11]]}},"alternative-id":["1028"],"URL":"https:\/\/doi.org\/10.1007\/s00371-014-1028-0","relation":{},"ISSN":["0178-2789","1432-2315"],"issn-type":[{"value":"0178-2789","type":"print"},{"value":"1432-2315","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,5]]}}}