{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,30]],"date-time":"2026-08-30T02:14:26Z","timestamp":1788056066308,"version":"build-2784847793"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,10,16]],"date-time":"2011-10-16T00:00:00Z","timestamp":1318723200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s11075-011-9507-0","type":"journal-article","created":{"date-parts":[[2011,10,15]],"date-time":"2011-10-15T08:37:38Z","timestamp":1318667858000},"page":"607-622","source":"Crossref","is-referenced-by-count":17,"title":["Polynomial approximation of rational B\u00e9zier curves with\u00a0constraints"],"prefix":"10.1007","volume":"59","author":[{"given":"Stanis\u0142aw","family":"Lewanowicz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pawe\u0142","family":"Wo\u017any","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pawe\u0142","family":"Keller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2011,10,16]]},"reference":[{"key":"9507_CR1","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/S0167-8396(03)00082-7","volume":"20","author":"YJ Ahn","year":"2003","unstructured":"Ahn, Y.J.: Using Jacobi polynomials for degree reduction of B\u00e9zier curves with C k -constraints. Comput. Aided Geom. Des. 20, 423\u2013434 (2003)","journal-title":"Comput. Aided Geom. Des."},{"key":"9507_CR2","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/j.cad.2009.12.008","volume":"42","author":"HJ Cai","year":"2010","unstructured":"Cai, H.J., Wang, G.J.: Constrained approximation of rational B\u00e9zier curves based on a matrix expression of its end points continuity condition. Comput. Aided Des. 42, 495\u2013504 (2010)","journal-title":"Comput. Aided Des."},{"key":"9507_CR3","doi-asserted-by":"crossref","unstructured":"Dahlquist, G., Bj\u00f6rck, A.: Numerical Methods in Scientific Computing, vol. I. SIAM, Philadelphia (2008)","DOI":"10.1137\/1.9780898717785"},{"key":"9507_CR4","volume-title":"Curves and Surfaces for Computer-Aided Geometric Design. A Practical Guide","author":"GE Farin","year":"1996","unstructured":"Farin, G.E.: Curves and Surfaces for Computer-Aided Geometric Design. A Practical Guide. Academic Press, Boston (1996)"},{"key":"9507_CR5","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/j.cagd.2006.06.003","volume":"23","author":"MS Floater","year":"2006","unstructured":"Floater, M.S.: High order approximation of rational curves by polynomial curves. Comput. Aided Des. 23, 621\u2013628 (2006)","journal-title":"Comput. Aided Des."},{"key":"9507_CR6","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1145\/355602.361310","volume":"15","author":"WM Gentleman","year":"1972","unstructured":"Gentleman, W.M.: Implementing Clenshaw\u2013Curtis quadrature\u2014I and II. Commun. ACM 15, 337\u2013346 (1972)","journal-title":"Commun. ACM"},{"key":"9507_CR7","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/j.cagd.2008.03.001","volume":"25","author":"Y Huang","year":"2008","unstructured":"Huang, Y., Su, H., Lin, H.: A simple method for approximating rational B\u00e9zier curve using B\u00e9zier curves. Comput. Aided Geom. Des. 25, 697\u2013699 (2008)","journal-title":"Comput. Aided Geom. Des."},{"key":"9507_CR8","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s11075-007-9134-y","volume":"46","author":"P Keller","year":"2007","unstructured":"Keller, P.: A method for indefinite integration of oscillatory and singular functions. Numer. Algorithms 46, 219\u2013251 (2007)","journal-title":"Numer. Algorithms"},{"key":"9507_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05014-5","volume-title":"Hypergeometric Orthogonal Polynomials and Their q-Analogues","author":"R Koekoek","year":"2010","unstructured":"Koekoek, R., Lesky, P., Swarttouw, R.F.: Hypergeometric Orthogonal Polynomials and Their q-Analogues. Springer, Berlin (2010)"},{"key":"9507_CR10","first-page":"88","volume":"2","author":"B-G Lee","year":"1998","unstructured":"Lee, B.-G., Park, Y.: Approximate conversion of rational B\u00e9zier curves. J. KSIAM 2, 88\u201393 (1998)","journal-title":"J. KSIAM"},{"key":"9507_CR11","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/0377-0427(92)90021-O","volume":"43","author":"S Lewanowicz","year":"1992","unstructured":"Lewanowicz, S.: Quick construction of recurrence relations for the Jacobi coefficients. J. Comput. Appl. Math. 43, 355\u2013372 (1992)","journal-title":"J. Comput. Appl. Math."},{"key":"9507_CR12","doi-asserted-by":"crossref","first-page":"4596","DOI":"10.1016\/j.amc.2010.11.011","volume":"217","author":"S Lewanowicz","year":"2011","unstructured":"Lewanowicz, S., Wo\u017any, P.: Multi-degree reduction of tensor product B\u00e9zier surfaces with general constraints. Appl. Math. Comput. 217, 4596\u20134611 (2011)","journal-title":"Appl. Math. Comput."},{"key":"9507_CR13","doi-asserted-by":"crossref","unstructured":"Lewanowicz, S., Wo\u017any, P.: B\u00e9zier representation of the constrained dual Bernstein polynomials. arXiv:1109.1169v1[math.NA] (2011)","DOI":"10.1016\/j.amc.2011.10.040"},{"key":"9507_CR14","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/GMAP.2000.838251","volume-title":"Proc. Geom. Modeling and Processing 2000: Theory and Applications","author":"LG Liu","year":"2000","unstructured":"Liu, L.G., Wang, G.J.: Recursive formulae for Hermite polynomial approximation to rational B\u00e9zier curves. In: Martin, R., Wang, W.P. (eds.) Proc. Geom. Modeling and Processing 2000: Theory and Applications, pp. 190\u2013197. IEEE Computer Society, Los Alamitos (2000)"},{"key":"9507_CR15","first-page":"127","volume":"27","author":"L Lu","year":"2010","unstructured":"Lu, L.: Weighted progressive iteration approximation of rational curves. Comput. Aided Geom. Des. 27, 127\u2013137 (2010)","journal-title":"Comput. Aided Geom. Des."},{"key":"9507_CR16","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1016\/j.cam.2010.08.008","volume":"235","author":"L Lu","year":"2011","unstructured":"Lu, L.: Sample-based polynomial approximation of rational B\u00e9zier curves. J. Comput. Appl. Math. 235, 1557\u20131563 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"9507_CR17","first-page":"144","volume-title":"NURBS for Curve and Surface Design","author":"TW Sederberg","year":"1991","unstructured":"Sederberg, T.W., Kakimoto, M.: Approximating rational curves using polynomial curves. In: Farin, G. (ed.) NURBS for Curve and Surface Design, pp. 144\u2013158. SIAM, Philadelphia (1991)"},{"key":"9507_CR18","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1137\/060659831","volume":"50","author":"LN Trefethen","year":"2008","unstructured":"Trefethen, L.N.: Is Gauss quadrature better than Clenshaw-Curtis? SIAM Rev. 50, 67\u201387 (2008)","journal-title":"SIAM Rev."},{"key":"9507_CR19","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1006\/jath.1996.3060","volume":"89","author":"GJ Wang","year":"1997","unstructured":"Wang, G.J., Sederberg, T.W., Chen, F.L.: On the convergence of polynomial approximation of rational functions. J. Approx. Theory 89, 267\u2013288 (1997)","journal-title":"J. Approx. Theory"},{"key":"9507_CR20","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.cagd.2009.01.006","volume":"26","author":"P Wo\u017any","year":"2009","unstructured":"Wo\u017any, P., Lewanowicz, S.: Multi-degree reduction of B\u00e9zier curves with constraints, using dual Bernstein basis polynomials. Comput. Aided Geom. Des. 26, 566\u2013579 (2009)","journal-title":"Comput. Aided Geom. Des."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-011-9507-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-011-9507-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-011-9507-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,17]],"date-time":"2019-06-17T15:55:28Z","timestamp":1560786928000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-011-9507-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,16]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["9507"],"URL":"https:\/\/doi.org\/10.1007\/s11075-011-9507-0","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,16]]}}}