{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T03:31:44Z","timestamp":1785900704391,"version":"3.56.0"},"reference-count":38,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1998,3,1]],"date-time":"1998-03-01T00:00:00Z","timestamp":888710400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computer Aided Geometric Design"],"published-print":{"date-parts":[[1998,3]]},"DOI":"10.1016\/s0167-8396(97)00024-1","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T15:03:07Z","timestamp":1027609387000},"page":"223-249","source":"Crossref","is-referenced-by-count":83,"title":["A Laguerre geometric approach to rational offsets"],"prefix":"10.1016","volume":"15","author":[{"given":"Martin","family":"Peternell","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Helmut","family":"Pottmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0167-8396(97)00024-1_BIB1","series-title":"Mathematical Methods for Curves and Surfaces","first-page":"1","article-title":"G2 approximation of an offset curve by Tschirnhausen quartics","author":"Ait Haddou","year":"1995"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB2","series-title":"Advances in Comp. Math.","article-title":"Construction of C2 Pythagorean-hodograph interpolating splines by the homotopy method","author":"Albrecht","year":"1996"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB3","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0010-4485(95)91139-C","article-title":"Curvature continuous connections of cones and cylinders","volume":"27","author":"Aumann","year":"1995","journal-title":"Computer-Aided Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF01693218","article-title":"Untersuchungen \u00fcber die Geometrie der Speere in der Euklidischen Ebene","volume":"21","author":"Blaschke","year":"1910","journal-title":"Monatshefte f\u00fcr Mathematik und Physik"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB5","series-title":"Vorlesungen \u00fcber differentialgeometrie III","author":"Blaschke","year":"1929"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB6","series-title":"Curves and Surfaces II","first-page":"1","article-title":"An Introduction to Pad\u00e9 Approximations","author":"Brezinski","year":"1993"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB7","series-title":"Lie Sphere Geometry","author":"Cecil","year":"1992"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB8","series-title":"NURBS for Curve and Surface Design","first-page":"35","article-title":"Rational B\u00e9zier curves and surfaces on projective domains","author":"DeRose","year":"1991"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB9","series-title":"Rationale B\u00e9zier-Kurven und B\u00e9zier-Fl\u00e4chenst\u00fccke auf Quadriken, dissertation","author":"Dietz","year":"1995"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB10","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0167-8396(93)90037-4","article-title":"An algebraic approach to curves and surfaces on the sphere and on other quadrics","volume":"10","author":"Dietz","year":"1993","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB11","series-title":"Geometry Processing for Design and Manufacturing","first-page":"3","article-title":"Pythagorean-hodograph curves in practical use","author":"Farouki","year":"1992"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB12","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0167-8396(94)90204-6","article-title":"The conformal map z \u21a6 z2 of the hodograph plane","volume":"11","author":"Farouki","year":"1994","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB13","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1090\/S0025-5718-1995-1308452-6","article-title":"Hermite interpolation by Pythagorean-hodograph quintics","volume":"64","author":"Farouki","year":"1995","journal-title":"Math. Comp."},{"key":"10.1016\/S0167-8396(97)00024-1_BIB14","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1147\/rd.345.0736","article-title":"Pythagorean hodographs","volume":"34","author":"Farouki","year":"1990","journal-title":"IBM J. Res. Develop."},{"key":"10.1016\/S0167-8396(97)00024-1_BIB15","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF02519035","article-title":"Pythagorean-hodograph space curves","volume":"2","author":"Farouki","year":"1994","journal-title":"Advances in Comp. Math."},{"key":"10.1016\/S0167-8396(97)00024-1_BIB16","first-page":"557","article-title":"Offset curves in layered manufacturing","volume":"Vol. 68-2","author":"Farouki","year":"1994","journal-title":"ASME PED"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB17","series-title":"Curves and Surfaces in Geometric Design","first-page":"153","article-title":"Characterization of the set of rational parametric curves with rational offsets","author":"Fiorot","year":"1994"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB18","series-title":"Mathematical Methods in CAGD III","first-page":"1","article-title":"Geometric Constraints for CAGD","author":"Hoffmann","year":"1995"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB19","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1115\/1.2826869","article-title":"Computer aided design with spatial rational B-spline motions","volume":"118","author":"J\u00fcttler","year":"1996","journal-title":"ASME J. of Mechanical Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB20","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF02663776","article-title":"Rationality of the offsets to algebraic curves and surfaces","volume":"9","author":"L\u00fc","year":"1994","journal-title":"Applied Mathematics"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB21","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/0167-8396(94)00036-R","article-title":"Offset-rational parametric plane curves","volume":"12","author":"L\u00fc","year":"1995","journal-title":"Computer Aided geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB22","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF02276876","article-title":"Rational parameterization of quadrics and their offsets","volume":"57","author":"L\u00fc","year":"1996","journal-title":"Computing"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB23","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/0167-8396(95)00051-8","article-title":"Pipe surfaces with rational spine curve are rational","volume":"13","author":"L\u00fc","year":"1996","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB24","article-title":"Principal patches for computational geometry","author":"Martin","year":"1982"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB25","series-title":"Advanced Topics in Multivariate Approximation","first-page":"275","article-title":"Designing rational surfaces with rational offsets","author":"Peternell","year":"1996"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB26","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1006\/jsco.1996.0087","article-title":"Computing rational parametrizations of canal surfaces","volume":"23","author":"Peternell","year":"1997","journal-title":"J. Symbolic Computation"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB27","series-title":"Curves and Surfaces in Geometric Design","first-page":"377","article-title":"Applications of the dual B\u00e9zier representation of rational curves and surfaces","author":"Pottmann","year":"1994"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB28","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0167-8396(94)00008-G","article-title":"Rational curves and surfaces with rational offsets","volume":"12","author":"Pottmann","year":"1995","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB29","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF03028365","article-title":"Curve design with rational Pythagorean-hodograph curves","volume":"3","author":"Pottmann","year":"1995","journal-title":"Advances in Comp. Math."},{"key":"10.1016\/S0167-8396(97)00024-1_BIB30","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/0167-8396(94)00031-M","article-title":"Developable rational B\u00e9zier and B-spline surfaces","volume":"12","author":"Pottmann","year":"1995","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB31","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1006\/gmip.1996.0045","article-title":"Rational ruled surfaces and their offsets","volume":"58","author":"Pottmann","year":"1996","journal-title":"Graphical Models and Image Processing"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB32","article-title":"Applications of Laguerre geometry in CAGD","author":"Pottmann","year":"1997","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB33","series-title":"The Mathematics of Surfaces VII","article-title":"Principal Surfaces","author":"Pottmann","year":"1997"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB34","series-title":"Acta Eruditorum","first-page":"68","article-title":"Methodus curvas determinandi, quae formantur a radiis reflectis, quorum incidentes ut paralleli considerantur","author":"Tschirnhaus","year":"1690"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB35","series-title":"Recent Advances in Robot Kinematics","first-page":"151","article-title":"Computer aided design of robot trajectories using rational Frenet-Serret motions","author":"Wagner","year":"1996"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB36","doi-asserted-by":"crossref","DOI":"10.1016\/S0167-8396(96)00037-4","article-title":"Rational blending surfaces between quadrics","author":"Wallner","year":"1997","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0167-8396(97)00024-1_BIB37","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01320498","article-title":"Spiegelung am elliptischen Paraboloid","volume":"52","author":"Wunderlich","year":"1948","journal-title":"Monatsh. Math."},{"key":"10.1016\/S0167-8396(97)00024-1_BIB38","first-page":"353","article-title":"Algebraische B\u00f6schungslinien dritter und vierter Ordnung","volume":"181","author":"Wunderlich","year":"1973","journal-title":"Sitzungsberichte der \u00d6sterreichischen Akademie der Wissenschaften"}],"container-title":["Computer Aided Geometric Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167839697000241?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167839697000241?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T23:22:46Z","timestamp":1555975366000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167839697000241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,3]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,3]]}},"alternative-id":["S0167839697000241"],"URL":"https:\/\/doi.org\/10.1016\/s0167-8396(97)00024-1","relation":{},"ISSN":["0167-8396"],"issn-type":[{"value":"0167-8396","type":"print"}],"subject":[],"published":{"date-parts":[[1998,3]]}}}