{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,21]],"date-time":"2023-05-21T04:45:04Z","timestamp":1684644304177},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,5,20]],"date-time":"2023-05-20T00:00:00Z","timestamp":1684540800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,20]],"date-time":"2023-05-20T00:00:00Z","timestamp":1684540800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s11424-023-1286-x","type":"journal-article","created":{"date-parts":[[2023,5,20]],"date-time":"2023-05-20T05:01:42Z","timestamp":1684558902000},"page":"1302-1318","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interactive Design of Cubic IPH Spline Curves"],"prefix":"10.1007","volume":"36","author":[{"given":"Jingjing","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,20]]},"reference":[{"key":"1286_CR1","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1016\/S0010-4485(98)00020-7","volume":"30","author":"RT Farouki","year":"1998","unstructured":"Farouki RT, Manjunathaiah J, Nichlas D, et al., Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves, Computer-Aided Design, 1998, 30: 631\u2013640.","journal-title":"Computer-Aided Design"},{"key":"1286_CR2","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1016\/0167-8396(95)00047-X","volume":"13","author":"R T Farouki","year":"1996","unstructured":"Farouki R T and Shah S, Real-time CNC interpolators for Pythagorean-hodograph curves, Computer Aided Geometric Design, 1996, 13: 583\u2013600.","journal-title":"Computer Aided Geometric Design"},{"key":"1286_CR3","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/S0167-8396(01)00029-2","volume":"18","author":"Y F Tsai","year":"2001","unstructured":"Tsai Y F, Farouki R T, and Feldman B, Performance analysis of CNC interpolators for time-dependent feedrates along PH curves, Computer Aided Geometric Design, 2001, 18: 245\u2013265.","journal-title":"Computer Aided Geometric Design"},{"issue":"1","key":"1286_CR4","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/S0010-4485(98)00080-3","volume":"31","author":"H I Choi","year":"1999","unstructured":"Choi H I, Han C Y, Moon H P, et al., Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves, Computer-Aided Design, 1999, 31(1): 59\u201372.","journal-title":"Computer-Aided Design"},{"key":"1286_CR5","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/S0010-4485(98)00081-5","volume":"31","author":"B J\u00fcttler","year":"1999","unstructured":"J\u00fcttler B and M\u00e4urer C, Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling, Computer-Aided Design, 1999, 31: 73\u201383.","journal-title":"Computer-Aided Design"},{"issue":"2","key":"1286_CR6","first-page":"141","volume":"3","author":"C M\u00e4urer","year":"1999","unstructured":"M\u00e4urer C and J\u00fcttler B, Rational approximation of rotation minimizing frames using Pythagorean-hodograph cubics, Journal for Geometry and Graphics, 1999, 3(2): 141\u2013159.","journal-title":"Journal for Geometry and Graphics"},{"issue":"6","key":"1286_CR7","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1016\/S1524-0703(03)00002-X","volume":"64","author":"R T Farouki","year":"2002","unstructured":"Farouki R T, Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves, Graphical Models, 2002, 64(6): 382\u2013395.","journal-title":"Graphical Models"},{"issue":"1","key":"1286_CR8","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0167-8396(98)00032-6","volume":"16","author":"R T Farouki","year":"1999","unstructured":"Farouki R T, Tsai Y F, and Yuan G F, Contour machining of free-form surfaces with real-time PH curve CNC interpolators, Computer Aided Geometric Design, 1999, 16(1): 61\u201376.","journal-title":"Computer Aided Geometric Design"},{"key":"1286_CR9","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1147\/rd.345.0736","volume":"34","author":"R T Farouki","year":"1990","unstructured":"Farouki R T and Sakkalis T, Pythagorean hodographs, IBM J. Res. Develop., 1990, 34: 736\u2013752.","journal-title":"IBM J. Res. Develop."},{"key":"1286_CR10","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/BF02519035","volume":"2","author":"R T Farouki","year":"1994","unstructured":"Farouki R T and Sakkalis T, Pythagorean-hodograph space curves, Adv. Comp. Math., 1994, 2: 41\u201366.","journal-title":"Adv. Comp. Math."},{"key":"1286_CR11","doi-asserted-by":"crossref","unstructured":"Farouki R T, Pythagorean hodograph curves in practical use, Ed. by Barnhill R E, Geometry Processing for Design and Manufacturing, SIAM, 1992, 3\u201333.","DOI":"10.1137\/1.9781611971668.ch1"},{"key":"1286_CR12","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/B978-044451104-1\/50018-6","volume-title":"Handbook of Computer Aided Geometric Design","author":"R T Farouki","year":"2002","unstructured":"Farouki R T, Pythagorean-hodograph curves, Eds. by Farin G, Hoschek J, Kim M S, Handbook of Computer Aided Geometric Design, Elsevier, Amsterdam, 2002, 405\u2013427."},{"key":"1286_CR13","doi-asserted-by":"crossref","unstructured":"Farouki R T, Pythagorean-hodograph curves: Algebra and geometry inseparable, Volume 1 of the series Geometry and Computing, 2008, 381\u2013391.","DOI":"10.1007\/978-3-540-73398-0_17"},{"key":"1286_CR14","doi-asserted-by":"publisher","first-page":"1006","DOI":"10.1016\/j.cagd.2009.08.003","volume":"26","author":"G Z Wang","year":"2009","unstructured":"Wang G Z and Fang L C, On control polygons of quartic Pythagorean-hodograph curves, Computer Aided Geometric Design, 2009, 26: 1006\u20131015.","journal-title":"Computer Aided Geometric Design"},{"key":"1286_CR15","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.cagd.2006.09.005","volume":"24","author":"F Pelosi","year":"2007","unstructured":"Pelosi F, Sampoli M L, and Farouki R T, A control polygon scheme for design of planar C2 PH quintic spline curves, Computer Aided Geometric Design, 2007, 24: 28\u201352.","journal-title":"Computer Aided Geometric Design"},{"key":"1286_CR16","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/j.cam.2015.09.006","volume":"296","author":"Z H Zheng","year":"2016","unstructured":"Zheng Z H, Wang G Z, and Yang P, On control polygons of Pythagorean hodograph septic curves, Journal of Computational and Applied Mathematics, 2016, 296: 212\u2013227.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"1286_CR17","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/BF02124754","volume":"5","author":"G Albrecht","year":"1996","unstructured":"Albrecht G and Farouki R T, Construction of C2 Pythagorean hodograph interpolating splines by the homotopy method, Adv. Comp. Math., 1996, 5: 417\u2013442.","journal-title":"Adv. Comp. Math."},{"issue":"6","key":"1286_CR18","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1016\/0167-8396(94)00038-T","volume":"12","author":"R T Farouki","year":"1995","unstructured":"Farouki R T and Sederberg T W, Analysis of the offset to a parabola, Computer Aided Geometry Design, 1995, 12(6): 639\u2013645.","journal-title":"Computer Aided Geometry Design"},{"issue":"6","key":"1286_CR19","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1016\/0167-8396(94)00036-R","volume":"12","author":"W Lu","year":"1995","unstructured":"Lu W, Offset-rational parametric plane curves, Comput. Aided Geom. Design, 1995, 12(6): 601\u2013616.","journal-title":"Comput. Aided Geom. Design"},{"key":"1286_CR20","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.cad.2015.07.006","volume":"70","author":"X J Lu","year":"2016","unstructured":"Lu X J, Zheng J M, Cai Y Y, et al., Geometric characteristics of a class of cubic curves with rational offsets, Computer-Aided Design, 2016, 70: 36\u201345.","journal-title":"Computer-Aided Design"},{"key":"1286_CR21","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/S0167-8396(01)00016-4","volume":"18","author":"P M Hwan","year":"2001","unstructured":"Hwan P M, Farouki R T, and Hyeong I C, Construction and shape analysis of PH quintic Hermite interpolants, Comput. Aided Geom. Design, 2001, 18: 93\u2013115.","journal-title":"Comput. Aided Geom. Design"},{"key":"1286_CR22","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/j.cagd.2007.03.010","volume":"25","author":"I C Hyeong","year":"2008","unstructured":"Hyeong I C, Farouki R T, Song H K, et al., Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants, Comput. Aided Geom. Design, 2008, 25: 411\u2013433.","journal-title":"Comput. Aided Geom. Design"},{"key":"1286_CR23","volume-title":"Curves and Surfaces for Computer Aided Geometric Design","author":"G Farin","year":"1997","unstructured":"Farin G, Curves and Surfaces for Computer Aided Geometric Design, 4th Ed. Academic Press, SanDiego, 1997.","edition":"4th Ed"},{"issue":"1\u20134","key":"1286_CR24","first-page":"83","volume":"7","author":"T Rid","year":"1990","unstructured":"Rid T, Farouki, and Neff C A, Analytic properties of plane offset curves, Compututer Aided Geometric Design, 1990, 7(1\u20134): 83\u201389.","journal-title":"Compututer Aided Geometric Design"},{"key":"1286_CR25","volume-title":"Handbook of Computer Aided Geometric Design","author":"G Farin","year":"2002","unstructured":"Farin G, Hoschek J, and Kim M, Handbook of Computer Aided Geometric Design, Elsevier, Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, the Netherlands, 2002."},{"key":"1286_CR26","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0167-8396(94)90204-6","volume":"11","author":"R T Farouki","year":"1994","unstructured":"Farouki R T, The conformal map z \u2192 z2 of the hodograph plane, Comput. Aided Geom. Design, 1994, 11: 363\u2013390.","journal-title":"Comput. Aided Geom. Design"},{"key":"1286_CR27","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0377-0427(97)00066-6","volume":"81","author":"D S Meek","year":"1997","unstructured":"Meek D S and Walton D J, Geometric Hermite interpolation with Tschirnhausen cubics, J. Comput. Appl. Math., 1997, 81: 299\u2013309.","journal-title":"J. Comput. Appl. Math."},{"key":"1286_CR28","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.1016\/j.cad.2012.04.007","volume":"44","author":"Y J Li","year":"2012","unstructured":"Li Y J and Deng C Y, C-shaped G2 Hermite interpolation with circular precision based on cubic PH curve interpolation, Comput. Aided Des., 2012, 44: 1056\u20131061.","journal-title":"Comput. Aided Des."},{"key":"1286_CR29","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1016\/j.cagd.2006.01.004","volume":"23","author":"J Kosinka","year":"2006","unstructured":"Kosinka J and J\u2019\u00fattler B, G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics, Computer Aided Geometric Design, 2006, 23: 401\u2013418.","journal-title":"Computer Aided Geometric Design"},{"key":"1286_CR30","doi-asserted-by":"publisher","first-page":"1589","DOI":"10.1090\/S0025-5718-1995-1308452-6","volume":"64","author":"R T Farouki","year":"1995","unstructured":"Farouki R T and Neff C A, Hermite interpolation by Pythagorean hodograph quintics, Math. Comp., 1995, 64: 1589\u20131609.","journal-title":"Math. Comp."},{"key":"1286_CR31","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/S0167-8396(01)00016-4","volume":"18","author":"H P Moon","year":"2001","unstructured":"Moon H P, Farouki R T, and Choi H I, Construction and shape analysis of PH quintic Hermite interpolants, Computer Aided Geometric Design, 2001, 18: 93\u2013115.","journal-title":"Computer Aided Geometric Design"},{"key":"1286_CR32","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1090\/S0025-5718-00-01288-6","volume":"70","author":"B J\u00fcttler","year":"2000","unstructured":"J\u00fcttler B, Hermite interpolation by Pythagorean hodograph curves of degree seven, Math. Comp., 2000, 70: 1089\u20131111.","journal-title":"Math. Comp."},{"key":"1286_CR33","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1023\/A:1016621116240","volume":"27","author":"R T Farouki","year":"2001","unstructured":"Farouki R T, Kuspa B K, Manni C, et al., Efficient solution of the complex quadratic tridiagonal system for C2 PH quintic splines, Numer. Algor., 2001, 27: 35\u201360.","journal-title":"Numer. Algor."},{"key":"1286_CR34","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s10444-015-9419-y","volume":"42","author":"R T Farouki","year":"2016","unstructured":"Farouki R T, Giannelli Carlotta, and Alessandra S, Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form, Adv. Comput. Math., 2016, 42: 199\u2013225.","journal-title":"Adv. Comput. Math."},{"issue":"4","key":"1286_CR35","doi-asserted-by":"publisher","first-page":"28.1","DOI":"10.1145\/2699467","volume":"41","author":"B H Dong","year":"2015","unstructured":"Dong B H and Farouki R T, PHquintic: A library of basic functions for the construction and analysis of planar quintic Pythagorean-Hodograph curves, ACM Transactions on Mathematical Software (TOMS), 2015, 41(4): 28.1\u201328.20.","journal-title":"ACM Transactions on Mathematical Software (TOMS)"},{"key":"1286_CR36","doi-asserted-by":"crossref","unstructured":"Verhoosel C V, Scott M A, Borden M J, et al., Isogeometric Failure Analysis, Recent Developments and Innovative Applications in Computational Mechanics, Springer Verlag, 2011, 275\u2013281.","DOI":"10.1007\/978-3-642-17484-1_31"},{"key":"1286_CR37","doi-asserted-by":"crossref","unstructured":"Burkhart D, Hamann B, and Umlauf G, Iso-geometric Finite Element Analysis Based on Catmull-Clark: Ubdivision Solids, Computer Graphics Forum, 1467\u20138659, Wiley Online Library, 1575\u20131584, 29, 2010.","DOI":"10.1111\/j.1467-8659.2010.01766.x"},{"key":"1286_CR38","unstructured":"Wells G N, Discontinuous modelling of strain localisation and failure, Delft University of Technology, Doctoral Thesis, 2001."},{"key":"1286_CR39","doi-asserted-by":"crossref","unstructured":"Schumaker L L, On the Dimension of Spaces of Piecewise Polynomials in Two Variables, Multivariate Approximation Theory, Birkhauser Verlag, Basel, Eds. by Schempp W, Zeller K, 1979, 396\u2013412.","DOI":"10.1007\/978-3-0348-6289-9_26"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-023-1286-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-023-1286-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-023-1286-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,20]],"date-time":"2023-05-20T05:16:18Z","timestamp":1684559778000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-023-1286-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,20]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["1286"],"URL":"https:\/\/doi.org\/10.1007\/s11424-023-1286-x","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,20]]},"assertion":[{"value":"9 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}