{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T08:26:15Z","timestamp":1759134375509},"publisher-location":"Berlin, Heidelberg","reference-count":22,"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_27","type":"book-chapter","created":{"date-parts":[[2012,1,6]],"date-time":"2012-01-06T06:00:11Z","timestamp":1325829611000},"page":"431-444","source":"Crossref","is-referenced-by-count":1,"title":["On a Special Class of Polynomial Surfaces with Pythagorean Normal Vector Fields"],"prefix":"10.1007","author":[{"given":"Miroslav","family":"L\u00e1vi\u010dka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Vr\u0161ek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"2","key":"27_CR1","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/0167-8396(94)00008-G","volume":"12","author":"H. Pottmann","year":"1995","unstructured":"Pottmann, H.: Rational curves and surfaces with rational offsets. Computer Aided Geometric Design\u00a012(2), 175\u2013192 (1995)","journal-title":"Computer Aided Geometric Design"},{"issue":"5","key":"27_CR2","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":"27_CR3","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)"},{"key":"27_CR4","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/BF02276876","volume":"57","author":"W. L\u00fc","year":"1996","unstructured":"L\u00fc, W., Pottmann, H.: Rational parameterization of quadrics and their offsets. Computing\u00a057, 135\u2013147 (1996)","journal-title":"Computing"},{"key":"27_CR5","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":"27_CR6","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":"27_CR7","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/S0010-4485(99)00013-5","volume":"31","author":"T. Maekawa","year":"1999","unstructured":"Maekawa, T.: An overview of offset curves and surfaces. Computer-Aided Design\u00a031, 165\u2013173 (1999)","journal-title":"Computer-Aided Design"},{"key":"27_CR8","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"},{"issue":"6","key":"27_CR9","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":"27_CR10","first-page":"355","volume-title":"Proceedings of the 6th IMA Conference on the Mathematics of Surfaces","author":"R.T. Farouki","year":"1996","unstructured":"Farouki, R.T., Pottmann, H.: Polynomial and rational Pythagorean-hodograph curves reconciled. In: Proceedings of the 6th IMA Conference on the Mathematics of Surfaces, pp. 355\u2013378. Clarendon Press, New York (1996)"},{"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":"27_CR11"},{"issue":"6","key":"27_CR12","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1016\/0167-8396(94)00036-R","volume":"12","author":"W. L\u00fc","year":"1995","unstructured":"L\u00fc, W.: Offset-rational parametric plane curves. Comput. Aided Geom. Des.\u00a012(6), 601\u2013616 (1995)","journal-title":"Comput. Aided Geom. Des."},{"issue":"7","key":"27_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"},{"key":"27_CR14","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1016\/j.cagd.2007.05.003","volume":"25","author":"M. Peternell","year":"2008","unstructured":"Peternell, M., Odehnal, B.: Convolution surfaces of quadratic triangular B\u00e9zier surfaces. Computer Aided Geometric Design\u00a025, 116\u2013129 (2008)","journal-title":"Computer Aided Geometric Design"},{"key":"27_CR15","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.cad.2007.10.008","volume":"40","author":"B. Bastl","year":"2008","unstructured":"Bastl, B., J\u00fcttler, B., Kosinka, J., L\u00e1vi\u010dka, M.: Computing exact rational offsets of quadratic triangular B\u00e9zier surface patches. Computer-Aided Design\u00a040, 197\u2013209 (2008)","journal-title":"Computer-Aided Design"},{"key":"27_CR16","first-page":"339","volume-title":"The Mathematics of Surfaces. VIII. Proceedings of the 8th IMA Conference Held in Birmingham","author":"K. Ueda","year":"1998","unstructured":"Ueda, K.: Pythagorean-hodograph curves on isothermal surfaces. In: Cripps, R. (ed.) The Mathematics of Surfaces. VIII. Proceedings of the 8th IMA Conference Held in Birmingham, GB, pp. 339\u2013353. Information Geometers, Winchester (1998)"},{"key":"27_CR17","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1016\/j.cagd.2008.06.011","volume":"25","author":"M. L\u00e1vi\u010dka","year":"2008","unstructured":"L\u00e1vi\u010dka, M., Bastl, B.: PN surfaces and their convolutions with rational surfaces. Computer Aided Geometric Design\u00a025, 763\u2013774 (2008)","journal-title":"Computer Aided Geometric Design"},{"issue":"1","key":"27_CR18","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.cam.2007.04.026","volume":"216","author":"G.I. Kim","year":"2008","unstructured":"Kim, G.I., Lee, S.: Pythagorean-hodograph preserving mappings. J. Comput. Appl. Math.\u00a0216(1), 217\u2013226 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"27_CR19","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":"27_CR20","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":"27_CR21","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)"},{"key":"27_CR22","volume-title":"Curves and surfaces for CAGD: a practical guide","author":"G. Farin","year":"2002","unstructured":"Farin, G.: Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann Publishers Inc., San Francisco (2002)"}],"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_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T23:47:29Z","timestamp":1556063249000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-27413-8_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642274121","9783642274138"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-27413-8_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}