{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T19:13:49Z","timestamp":1768590829799,"version":"3.49.0"},"reference-count":30,"publisher":"Elsevier BV","issue":"8","license":[{"start":{"date-parts":[[1998,7,1]],"date-time":"1998-07-01T00:00:00Z","timestamp":899251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[1998,7,1]],"date-time":"1998-07-01T00:00:00Z","timestamp":899251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[1998,9,21]],"date-time":"1998-09-21T00:00:00Z","timestamp":906336000000},"content-version":"vor","delay-in-days":82,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer-Aided Design"],"published-print":{"date-parts":[[1998,7]]},"DOI":"10.1016\/s0010-4485(98)00020-7","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T22:58:05Z","timestamp":1027637885000},"page":"631-640","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":122,"title":["Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves"],"prefix":"10.1016","volume":"30","author":[{"given":"RidaT.","family":"Farouki","sequence":"first","affiliation":[]},{"given":"Jairam","family":"Manjunathaiah","sequence":"additional","affiliation":[]},{"given":"David","family":"Nicholas","sequence":"additional","affiliation":[]},{"given":"Guo-Feng","family":"Yuan","sequence":"additional","affiliation":[]},{"given":"Sungchul","family":"Jee","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0010-4485(98)00020-7_BIB1","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/BF02124754","article-title":"Construction of C2 Pythagorean-hodograph interpolating splines by the homotopy method","volume":"5","author":"Albrecht","year":"1996","journal-title":"Advances in Computational Mathematics"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB2","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1115\/1.2899701","article-title":"Command axis generation for threeaxis CNC machining","volume":"113","author":"Chou","year":"1991","journal-title":"ASME Journal of Engineering for Industry"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB3","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1115\/1.2899753","article-title":"On the generation of coordinated motion of five-axis CNC\/CMM machines","volume":"114","author":"Chou","year":"1992","journal-title":"ASME Journal of Engineering for Industry"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB4","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\/S0010-4485(98)00020-7_BIB5","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0167-8396(94)90204-6","article-title":"The conformal map z \u2192 z2 of the hodograph plane","volume":"11","author":"Farouki","year":"1994","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB6","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0167-8396(95)00024-0","article-title":"The elastic bending energy of Pythagorean-hodograph curves","volume":"13","author":"Farouki","year":"1996","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB7","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/S0010-4485(97)00004-3","article-title":"Pythagorean-hodograph quintic transition curves of monotone curvature","volume":"29","author":"Farouki","year":"1997","journal-title":"Computer-Aided Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB8","doi-asserted-by":"crossref","DOI":"10.1016\/S0094-114X(97)00099-2","article-title":"Design of rational cam profiles with Pythagorean-hodograph curves","author":"Farouki","year":"1998","journal-title":"Mechanism and Machine Theory"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB9","article-title":"Implementation and performance analysis of a real-time CNC interpolator for precision machining of Pythagorean-hodograph curves","author":"Farouki","year":"1997","journal-title":"ASME Journal of Manufacturing Science and Engineering"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB10","article-title":"G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC machines","author":"Farouki","year":"1998","journal-title":"International Journal of Machine Tools and Manufacture"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0167-8396(90)90023-K","article-title":"Analytic properties of plane offset curves, Algebraic properties of plane offset curves","volume":"7","author":"Farouki","year":"1990","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB12","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1090\/S0025-5718-1995-1308452-6","article-title":"Hermite interpolation by Pythagoreanhodograph quintics","volume":"64","author":"Farouki","year":"1995","journal-title":"Mathematics of Computation"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB13","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0167-8396(87)90012-4","article-title":"On the numerical condition of polynomials in Bernstein form","volume":"4","author":"Farouki","year":"1987","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-8396(88)90016-7","article-title":"Algorithms for polynomials in Bernstein form","volume":"5","author":"Farouki","year":"1988","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB15","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 Journal of Research and Development"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB16","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/0167-8396(95)00047-X","article-title":"Real-time CNC interpolators for Pythagorean-hodograph curves","volume":"13","author":"Farouki","year":"1996","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB17","article-title":"Contour machining of free-form surfaces with real-time PH curve CNC interpolators","author":"Farouki","year":"1998","journal-title":"Computer Aided Geometric Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB18","first-page":"377","article-title":"Computer generated CNC machining feed rates","volume":"Vol. 1","author":"Fussel","year":"1992"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB19","volume":"Vol. 1","author":"Henrici","year":"1974"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB20","first-page":"393","article-title":"A generalized interpolator for command generation of parametric curves in computer-controlled machines","volume":"Vol. 1","author":"Huang","year":"1992"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB21","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/TC.1976.5009202","article-title":"Interpolator for a computer numerical control system","volume":"C-25","author":"Koren","year":"1976","journal-title":"IEEE Transactions on Computers"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB22","author":"Koren","year":"1983"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB23","first-page":"145","article-title":"Real-time interpolators for multi-axis CNC machine tools","volume":"25","author":"Lin","year":"1996","journal-title":"Manufacturing Systems"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB24","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\/S0010-4485(98)00020-7_BIB25","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 Computational Mathematics"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB26","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/S0007-8506(07)60959-7","article-title":"A new method of NC interpolation for machining the sculptured surface","volume":"30","author":"Sata","year":"1981","journal-title":"Annals of the CIRP"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB27","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/0010-4485(94)90097-3","article-title":"Realtime curve interpolators","volume":"26","author":"Shpitalni","year":"1994","journal-title":"Computer-Aided Design"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB28","first-page":"156","article-title":"Graphical simulation and automatic verification of NC machining programs","volume":"Vol. 1","author":"Sungurtekin","year":"1986"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB29","first-page":"915","article-title":"Closing the loop in CAD\/CAM integration","volume":"Vol. 2","author":"Vann","year":"1988"},{"key":"10.1016\/S0010-4485(98)00020-7_BIB30","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0010-4485(94)90045-0","article-title":"Parametric interpolator versus linear interpolator for precision CNC machining","volume":"26","author":"Yang","year":"1994","journal-title":"Computer-Aided Design"}],"container-title":["Computer-Aided Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010448598000207?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010448598000207?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,14]],"date-time":"2025-09-14T18:40:10Z","timestamp":1757875210000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0010448598000207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,7]]},"references-count":30,"journal-issue":{"issue":"8","published-print":{"date-parts":[[1998,7]]}},"alternative-id":["S0010448598000207"],"URL":"https:\/\/doi.org\/10.1016\/s0010-4485(98)00020-7","relation":{},"ISSN":["0010-4485"],"issn-type":[{"value":"0010-4485","type":"print"}],"subject":[],"published":{"date-parts":[[1998,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves","name":"articletitle","label":"Article Title"},{"value":"Computer-Aided Design","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0010-4485(98)00020-7","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 1998 Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}