{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T15:56:26Z","timestamp":1768319786303,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T00:00:00Z","timestamp":1520380800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"none"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1007\/s10444-018-9599-3","type":"journal-article","created":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T06:04:56Z","timestamp":1520402696000},"page":"1627-1650","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Rational frames of minimal twist along space curves under specified boundary conditions"],"prefix":"10.1007","volume":"44","author":[{"given":"Rida T.","family":"Farouki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hwan Pyo","family":"Moon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,7]]},"reference":[{"key":"9599_CR1","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1080\/00029890.1975.11993807","volume":"82","author":"RL Bishop","year":"1975","unstructured":"Bishop, R.L.: There is more than one way to frame a curve. Amer. Math. Monthly 82, 246\u2013251 (1975)","journal-title":"Amer. Math. Monthly"},{"issue":"24","key":"9599_CR2","doi-asserted-by":"publisher","first-page":"Article 245101","DOI":"10.1063\/1.3273453","volume":"131","author":"LA Britton","year":"2009","unstructured":"Britton, L.A., Olson, W.K., Tobias, I.: Two perspectives on the twist of DNA. J. Chem. Phys. 131(24), Article 245101 (2009)","journal-title":"J. Chem. Phys."},{"key":"9599_CR3","unstructured":"Brent, R.P.: Algorithms for Minimization Without Derivatives. Dover (reprint). Mineola (1973)"},{"key":"9599_CR4","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1042\/BST20120346","volume":"41","author":"GS Chirikjian","year":"2013","unstructured":"Chirikjian, G.S.: Framed curves and knotted DNA. Biochem. Soc. Trans. 41, 635\u2013638 (2013)","journal-title":"Biochem. Soc. Trans."},{"key":"9599_CR5","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1016\/S0167-8396(02)00165-6","volume":"19","author":"HI Choi","year":"2002","unstructured":"Choi, H.I., Han, C.Y.: Euler\u2013Rodrigues frames on spatial Pythagorean\u2013hodograph curves. Comput. Aided Geom. Des. 19, 603\u2013620 (2002)","journal-title":"Comput. Aided Geom. Des."},{"key":"9599_CR6","doi-asserted-by":"publisher","first-page":"3245","DOI":"10.1098\/rspa.2005.1527","volume":"461","author":"MR Dennis","year":"2005","unstructured":"Dennis, M.R., Hannay, J.H.: Geometry of Calugareanu\u2019s theorem. Proc. Royal Soc. London Series A 461, 3245\u20133254 (2005)","journal-title":"Proc. Royal Soc. London Series A"},{"key":"9599_CR7","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 edn. Academic Press, San Diego (1997)","edition":"4th edn."},{"key":"9599_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73398-0","volume-title":"Pythagorean\u2013Hodograph Curves: Algebra and Geometry Inseperable","author":"RT Farouki","year":"2008","unstructured":"Farouki, R.T.: Pythagorean\u2013Hodograph Curves: Algebra and Geometry Inseperable. Springer, Berlin (2008)"},{"key":"9599_CR9","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s10444-009-9138-3","volume":"33","author":"RT Farouki","year":"2010","unstructured":"Farouki, R.T.: Quaternion and Hopf map characterizations for the existence of rational rotation\u2013minimizing frames on quintic space curves. Adv. Comp. Math. 33, 331\u2013348 (2010)","journal-title":"Adv. Comp. Math."},{"key":"9599_CR10","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.amc.2015.04.122","volume":"272","author":"RT Farouki","year":"2016","unstructured":"Farouki, R.T.: Rational rotation\u2013minimizing frames \u2014 Recent advances ond open problems. Appl. Math. Comp. 272, 80\u201391 (2016)","journal-title":"Appl. Math. Comp."},{"key":"9599_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10444-016-9473-0","volume":"43","author":"RT Farouki","year":"2017","unstructured":"Farouki, R.T., Gentili, G., Giannelli, C., Sestini, A., Stoppato, C.: A comprehensive characterization of the set of polynomial curves with rational rotation\u2013minimizing frames. Adv. Comp. Math. 43, 1\u201324 (2017)","journal-title":"Adv. Comp. Math."},{"key":"9599_CR12","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1016\/j.cagd.2007.09.007","volume":"25","author":"RT Farouki","year":"2008","unstructured":"Farouki, R.T., Giannelli, C., Manni, C., Sestini, A.: Identification of spatial PH quintic Hermite interpolants with near\u2013optimal shape measures. Comput. Aided Geom. Des. 25, 274\u2013297 (2008)","journal-title":"Comput. Aided Geom. Des."},{"key":"9599_CR13","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1090\/S0025-5718-2011-02519-6","volume":"81","author":"RT Farouki","year":"2012","unstructured":"Farouki, R.T., Giannelli, C., Manni, C., Sestini, A.: Design of rational rotation\u2013minimizing rigid body motions by Hermite interpolation. Math. Comp. 81, 879\u2013903 (2012)","journal-title":"Math. Comp."},{"key":"9599_CR14","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/S0167-8396(03)00095-5","volume":"20","author":"RT Farouki","year":"2003","unstructured":"Farouki, R.T., Han, C.Y.: Rational approximation schemes for rotation\u2013minimizing frames on Pythagorean\u2013hodograph curves. Comput. Aided Geom. Des. 20, 435\u2013454 (2003)","journal-title":"Comput. Aided Geom. Des."},{"key":"9599_CR15","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1016\/j.cagd.2013.03.001","volume":"30","author":"RT Farouki","year":"2013","unstructured":"Farouki, R.T., Han, C.Y., Dospra, P., Sakkalis, T.: Rotation\u2013minimizing Euler\u2013Rodrigues rigid\u2013body motion interpolants. Comput. Aided Geom. Des. 30, 653\u2013671 (2013)","journal-title":"Comput. Aided Geom. Des."},{"key":"9599_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0167-8396(88)90016-7","volume":"5","author":"RT Farouki","year":"1988","unstructured":"Farouki, R.T., Rajan, V.T.: Algorithms for polynomials in Bernstein form. Comput. Aided Geom. Des. 5, 1\u201326 (1988)","journal-title":"Comput. Aided Geom. Des."},{"key":"9599_CR17","doi-asserted-by":"publisher","first-page":"844","DOI":"10.1016\/j.jsc.2010.03.004","volume":"45","author":"RT Farouki","year":"2010","unstructured":"Farouki, R.T., Sakkalis, T.: Rational rotation\u2013minimizing frames on polynomial space curves of arbitrary degree. J. Symb. Comput. 45, 844\u2013856 (2010)","journal-title":"J. Symb. Comput."},{"key":"9599_CR18","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.jsc.2011.09.012","volume":"47","author":"RT Farouki","year":"2012","unstructured":"Farouki, R.T., Sakkalis, T.: A complete classification of quintic space curves with rational rotation\u2013minimizing frames. J. Symb. Comput. 47, 214\u2013226 (2012)","journal-title":"J. Symb. Comput."},{"key":"9599_CR19","unstructured":"J\u00fcttler, B.: Generating rational frames of space curves via Hermite interpolation with Pythagorean hodograph cubic splines. In: Geometric Modeling and Processing \u201998, pp. 83\u2013106. Bookplus Press (1998)"},{"key":"9599_CR20","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/978-94-015-9064-8_42","volume-title":"Advances in Robot Kinematics: Analysis and Control","author":"B. J\u00fcttler","year":"1998","unstructured":"J\u00fcttler, B.: Rotation minimizing spherical motions. In: Lenarcic, J., Husty, M.L. (eds.) Advances in Robot Kinematics: Analysis and Control, pp. 413\u2013422. Springer, Dordrecht (1998)"},{"key":"9599_CR21","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., M\u00e4urer, C.: Cubic Pythagorean hodograph spline curves and applications to sweep surface modelling. Comput. Aided Des. 31, 73\u201383 (1999)","journal-title":"Comput. Aided Des."},{"key":"9599_CR22","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1080\/08927020601024137","volume":"32","author":"JS Kim","year":"2006","unstructured":"Kim, J.S., Chirikjian, G.S.: Conformational analysis of stiff chiral polymers with end constraints. Molec. Simul. 32, 1139\u20131154 (2006)","journal-title":"Molec. Simul."},{"key":"9599_CR23","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0167-8396(86)90039-7","volume":"3","author":"F Klok","year":"1986","unstructured":"Klok, F.: Two moving coordinate frames for sweeping along a 3D trajectory. Comput. Aided Geom. Des. 3, 217\u2013229 (1986)","journal-title":"Comput. Aided Geom. Des."},{"key":"9599_CR24","doi-asserted-by":"publisher","first-page":"1696","DOI":"10.1016\/j.matcom.2012.04.003","volume":"82","author":"M Krajnc","year":"2012","unstructured":"Krajnc, M., Vitrih, V.: Motion design with Euler\u2013Rodrigues frames of quintic Pythagorean\u2013hodograph curves. Math. Comp. Simul. 82, 1696\u20131711 (2012)","journal-title":"Math. Comp. Simul."},{"key":"9599_CR25","doi-asserted-by":"crossref","unstructured":"Kreyszig, E.: Differential Geometry. University of Toronto Press (1959)","DOI":"10.3138\/9781487589455"},{"key":"9599_CR26","first-page":"141","volume":"3","author":"C M\u00e4urer","year":"1999","unstructured":"M\u00e4urer, C., J\u00fcttler, B.: Rational approximation of rotation minimizing frames using Pythagorean\u2013hodograph cubics. J. Geom. Graph. 3, 141\u2013159 (1999)","journal-title":"J. Geom. Graph."},{"key":"9599_CR27","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1007\/11537908_22","volume-title":"Mathematics of Surfaces XI","author":"Zbyn\u011bk \u0160\u00edr","year":"2005","unstructured":"Sir, Z., J\u00fcttler, B.: Spatial Pythagorean hodograph quintics and the approximation of pipe surfaces. In: Martin, R., Bez, H., Sabin, M. (eds.) Mathematics of Surfaces XI, pp. 364\u2013380. Springer, Berlin (2005)"},{"key":"9599_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21738-3","volume-title":"Introduction to Numerical Analysis","author":"J Stoer","year":"2002","unstructured":"Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, 3rd edn. Springer, New York (2002)","edition":"3rd edn."},{"key":"9599_CR29","volume-title":"Theory of Equations","author":"JV Uspensky","year":"1948","unstructured":"Uspensky, J.V.: Theory of Equations. McGraw\u2013Hill, New York (1948)"},{"key":"9599_CR30","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/S0010-4485(96)00077-2","volume":"29","author":"W Wang","year":"1997","unstructured":"Wang, W., Joe, B.: Robust computation of the rotation minimizing frame for sweep surface modelling. Comput. Aided Des. 29, 379\u2013391 (1997)","journal-title":"Comput. Aided Des."},{"key":"9599_CR31","first-page":"1","volume":"Article 2","author":"W Wang","year":"2008","unstructured":"Wang, W., J\u00fcttler, B., Zheng, D., Liu, Y.: Computation of rotation minimizing frames. ACM Trans. Graph. 27 Article 2, 1\u201318 (2008)","journal-title":"ACM Trans. Graph. 27"},{"key":"9599_CR32","first-page":"1785","volume":"17","author":"Z Zheng","year":"2005","unstructured":"Zheng, Z., Wang, G.: Constructing rotation\u2013minimizing frame of space B\u00e9zier curve. J. Comput. Aided Des.& Comput. Graph. 17, 1785\u20131792 (2005)","journal-title":"J. Comput. Aided Des.& Comput. Graph."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-018-9599-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-018-9599-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-018-9599-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:34:26Z","timestamp":1551918866000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-018-9599-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,7]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["9599"],"URL":"https:\/\/doi.org\/10.1007\/s10444-018-9599-3","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,7]]},"assertion":[{"value":"7 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}