{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T19:13:48Z","timestamp":1725650028101},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642274121"},{"type":"electronic","value":"9783642274138"}],"license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-27413-8_45","type":"book-chapter","created":{"date-parts":[[2012,1,6]],"date-time":"2012-01-06T01:00:11Z","timestamp":1325811611000},"page":"681-696","source":"Crossref","is-referenced-by-count":0,"title":["Algebraic Curves of Low Convolution Degree"],"prefix":"10.1007","author":[{"given":"Jan","family":"Vr\u0161ek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miroslav","family":"L\u00e1vi\u010dka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"6","key":"45_CR1","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1016\/j.jsc.2010.02.001","volume":"45","author":"J. Vr\u0161ek","year":"2010","unstructured":"Vr\u0161ek, J., L\u00e1vi\u010dka, M.: On convolution of algebraic curves. Journal of Symbolic Computation\u00a045(6), 657\u2013676 (2010)","journal-title":"Journal of Symbolic Computation"},{"key":"45_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73398-0","volume-title":"Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable","author":"R. Farouki","year":"2008","unstructured":"Farouki, R.: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Springer, Heidelberg (2008)"},{"issue":"5","key":"45_CR3","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1147\/rd.345.0736","volume":"34","author":"R. Farouki","year":"1990","unstructured":"Farouki, R., Sakkalis, T.: Pythagorean hodographs. IBM Journal of Research and Development\u00a034(5), 736\u2013752 (1990)","journal-title":"IBM Journal of Research and Development"},{"key":"45_CR4","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/BF02519035","volume":"2","author":"R. Farouki","year":"1994","unstructured":"Farouki, R., Sakkalis, T.: Pythagorean-hodograph space curves. Adv. Comput. Math.\u00a02, 41\u201366 (1994)","journal-title":"Adv. Comput. Math."},{"key":"45_CR5","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., J\u00fcttler, B.: G\n                1 Hermite interpolation by Minkowski Pythagorean hodograph cubics. Computer Aided Geometric Design\u00a023, 401\u2013418 (2006)","journal-title":"Computer Aided Geometric Design"},{"key":"45_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/978-3-540-73843-5_15","volume-title":"Mathematics of Surfaces XII","author":"J. Kosinka","year":"2007","unstructured":"Kosinka, J., J\u00fcttler, B.: MOS surfaces: Medial surface transforms with rational domain boundaries. In: Martin, R., Sabin, M.A., Winkler, J.R. (eds.) Mathematics of Surfaces 2007. LNCS, vol.\u00a04647, pp. 245\u2013262. Springer, Heidelberg (2007)"},{"issue":"7","key":"45_CR7","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/j.cagd.2010.06.003","volume":"27","author":"J. Kosinka","year":"2010","unstructured":"Kosinka, J., L\u00e1vi\u010dka, M.: On rational Minkowski Pythagorean hodograph curves. Computer Aided Geometric Design\u00a027(7), 514\u2013524 (2010)","journal-title":"Computer Aided Geometric Design"},{"key":"45_CR8","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/S0167-8396(97)00024-1","volume":"15","author":"M. Peternell","year":"1998","unstructured":"Peternell, M., Pottmann, H.: A Laguerre geometric approach to rational offsets. Computer Aided Geometric Design\u00a015, 223\u2013249 (1998)","journal-title":"Computer Aided Geometric Design"},{"key":"45_CR9","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/S0167-8396(97)00023-X","volume":"15","author":"H. Pottmann","year":"1998","unstructured":"Pottmann, H., Peternell, M.: Applications of Laguerre geometry in CAGD. Computer Aided Geometric Design\u00a015, 165\u2013186 (1998)","journal-title":"Computer Aided Geometric Design"},{"unstructured":"J\u00fcttler, B.: Triangular B\u00e9zier surface patches with linear normal vector field. In: Cripps, R. (ed.) The Mathematics of Surfaces VIII. Information Geometers, pp. 431\u2013446 (1998)","key":"45_CR10"},{"issue":"2","key":"45_CR11","first-page":"157","volume":"7","author":"M. Peternell","year":"2003","unstructured":"Peternell, M., Manhart, F.: The convolution of a paraboloid and a parametrized surface. Journal for Geometry and Graphics\u00a07(2), 157\u2013171 (2003)","journal-title":"Journal for Geometry and Graphics"},{"issue":"2","key":"45_CR12","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.cagd.2005.07.001","volume":"23","author":"M.L. Sampoli","year":"2006","unstructured":"Sampoli, M.L., Peternell, M., J\u00fcttler, B.: Rational surfaces with linear normals and their convolutions with rational surfaces. Computer Aided Geometric Design\u00a023(2), 179\u2013192 (2006)","journal-title":"Computer Aided Geometric Design"},{"issue":"7","key":"45_CR13","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1016\/j.cagd.2007.04.006","volume":"24","author":"M. L\u00e1vi\u010dka","year":"2007","unstructured":"L\u00e1vi\u010dka, M., Bastl, B.: Rational hypersurfaces with rational convolutions. Computer Aided Geometric Design\u00a024(7), 410\u2013426 (2007)","journal-title":"Computer Aided Geometric Design"},{"issue":"2","key":"45_CR14","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1006\/gmip.1998.0464","volume":"60","author":"I.K. Lee","year":"1998","unstructured":"Lee, I.K., Kim, M.S., Elber, G.: Polynomial\/rational approximation of Minkowski sum boundary curves. Graphical Models and Image Processing\u00a060(2), 136\u2013165 (1998)","journal-title":"Graphical Models and Image Processing"},{"key":"45_CR15","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.cagd.2007.10.005","volume":"25","author":"J. Gravesen","year":"2008","unstructured":"Gravesen, J., J\u00fcttler, B., \u0160\u00edr, Z.: On rationally supported surfaces. Computer Aided Geometric Design\u00a025, 320\u2013331 (2008)","journal-title":"Computer Aided Geometric Design"},{"issue":"1-3","key":"45_CR16","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.tcs.2007.10.009","volume":"392","author":"Z. \u0160\u00edr","year":"2008","unstructured":"\u0160\u00edr, Z., Gravesen, J., J\u00fcttler, B.: Curves and surfaces represented by polynomial support functions. Theoretical Computer Science\u00a0392(1-3), 141\u2013157 (2008)","journal-title":"Theoretical Computer Science"},{"key":"45_CR17","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1006\/jsco.1996.0088","volume":"23","author":"E. Arrondo","year":"1997","unstructured":"Arrondo, E., Sendra, J., Sendra, J.R.: Parametric generalized offsets to hypersurfaces. Journal of Symbolic Computation\u00a023, 267\u2013285 (1997)","journal-title":"Journal of Symbolic Computation"},{"key":"45_CR18","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/S0022-4049(98)00028-0","volume":"136","author":"E. Arrondo","year":"1999","unstructured":"Arrondo, E., Sendra, J., Sendra, J.R.: Genus formula for generalized offset curves. Journal of Pure and Applied Algebra\u00a0136, 199\u2013209 (1999)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"45_CR19","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1007\/s002090050004","volume":"237","author":"J.R. Sendra","year":"2000","unstructured":"Sendra, J.R., Sendra, J.: Algebraic analysis of offsets to hypersurfaces. Mathematische Zeitschrift\u00a0237, 697\u2013719 (2000)","journal-title":"Mathematische Zeitschrift"},{"key":"45_CR20","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.cagd.2010.02.001","volume":"27","author":"Z. \u0160\u00edr","year":"2010","unstructured":"\u0160\u00edr, Z., Bastl, B., L\u00e1vi\u010dka, M.: Hermite interpolation by hypocycloids and epicycloids with rational offsets. Computer Aided Geometric Design\u00a027, 405\u2013417 (2010)","journal-title":"Computer Aided Geometric Design"},{"key":"45_CR21","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1090\/S0025-5718-00-01288-6","volume":"70","author":"B. J\u00fcttler","year":"2001","unstructured":"J\u00fcttler, B.: Hermite interpolation by Pythagorean hodograph curves of degree seven. Math. Comp.\u00a070, 1089\u20131111 (2001)","journal-title":"Math. Comp."},{"key":"45_CR22","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/S0167-8396(00)00002-9","volume":"17","author":"B. J\u00fcttler","year":"2000","unstructured":"J\u00fcttler, B., Sampoli, M.: Hermite interpolation by piecewise polynomial surfaces with rational offsets. Computer Aided Geometric Design\u00a017, 361\u2013385 (2000)","journal-title":"Computer Aided Geometric Design"},{"issue":"2","key":"45_CR23","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., Walton, D.J.: Geometric Hermite interpolation with Tschirnhausen cubics. J. Comput. Appl. Math.\u00a081(2), 299\u2013309 (1997)","journal-title":"J. Comput. Appl. Math."},{"key":"45_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5097-1","volume-title":"Plane algebraic curves","author":"E. Brieskorn","year":"1986","unstructured":"Brieskorn, E., Kn\u00f6rer, H.: Plane algebraic curves. Birkha\u00fcser, Basel (1986)"},{"key":"45_CR25","volume-title":"Using algebraic geometry","author":"D.A. Cox","year":"2005","unstructured":"Cox, D.A., Little, J., O\u2019Shea, D.: Using algebraic geometry, 2nd edn. Springer, Heidelberg (2005)","edition":"2"},{"key":"45_CR26","volume-title":"Algebraic Curves","author":"W. Fulton","year":"1969","unstructured":"Fulton, W.: Algebraic Curves. Benjamin, New York (1969)"},{"key":"45_CR27","first-page":"82","volume-title":"Proceedings of the 9th IMA Conference on the Mathematics of Surfaces","author":"M.S. Kim","year":"2000","unstructured":"Kim, M.S., Elber, G.: Problem reduction to parameter space. In: Proceedings of the 9th IMA Conference on the Mathematics of Surfaces, pp. 82\u201398. Springer, Heidelberg (2000)"},{"key":"45_CR28","volume-title":"Algebraic Curves","author":"R. Walker","year":"1950","unstructured":"Walker, R.: Algebraic Curves. Princeton University Press, Princeton (1950)"},{"key":"45_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/978-3-642-11620-9_19","volume-title":"Mathematical Methods for Curves and Surfaces","author":"M. L\u00e1vi\u010dka","year":"2010","unstructured":"L\u00e1vi\u010dka, M., Bastl, B., \u0160\u00edr, Z.: Reparameterization of curves and surfaces with respect to their convolution. In: D\u00e6hlen, M., Floater, M., Lyche, T., Merrien, J.-L., M\u00f8rken, K., Schumaker, L.L. (eds.) MMCS 2008. LNCS, vol.\u00a05862, pp. 285\u2013298. Springer, Heidelberg (2010)"},{"doi-asserted-by":"crossref","unstructured":"Cohen, H., Frey, G. (eds.): Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman & Hall\/CRC (2005)","key":"45_CR30","DOI":"10.1201\/9781420034981"},{"key":"45_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3849-0","volume-title":"Algebraic Geometry","author":"R. Hartshorne","year":"1977","unstructured":"Hartshorne, R.: Algebraic Geometry. Springer, Heidelberg (1977)"},{"key":"45_CR32","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1016\/S0167-8396(99)00016-3","volume":"16","author":"H. Moon","year":"1999","unstructured":"Moon, H.: Minkowski Pythagorean hodographs. Computer Aided Geometric Design\u00a016, 739\u2013753 (1999)","journal-title":"Computer Aided Geometric Design"}],"container-title":["Lecture Notes in Computer Science","Curves and Surfaces"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-27413-8_45","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T19:50:33Z","timestamp":1556049033000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-27413-8_45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642274121","9783642274138"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-27413-8_45","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}