{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T21:50:21Z","timestamp":1773265821195,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,7,1]],"date-time":"2000-07-01T00:00:00Z","timestamp":962409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Computational Mathematics"],"published-print":{"date-parts":[[2000,7]]},"DOI":"10.1023\/a:1018910412112","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T22:07:13Z","timestamp":1045692433000},"page":"199-229","source":"Crossref","is-referenced-by-count":23,"title":["Algorithms for Minkowski products and implicitly\u2010defined complex sets"],"prefix":"10.1007","volume":"13","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"}]},{"given":"Bahram","family":"Ravani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"325394_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139172615","volume-title":"Curves and Singularities","author":"J.W. Bruce","year":"1992","unstructured":"J.W. Bruce and P.J. Giblin, Curves and Singularities, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).","edition":"2nd ed."},{"key":"325394_CR2","volume-title":"Introduction to the Geometry of Complex Numbers","author":"R. Deaux","year":"1956","unstructured":"R. Deaux, Introduction to the Geometry of Complex Numbers (translated from the French by H. Eves) (F. Ungar, New York, 1956)."},{"key":"325394_CR3","volume-title":"Differential Geometry of Curves and Surfaces","author":"M.P. do Carmo","year":"1976","unstructured":"M.P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976)."},{"key":"325394_CR4","volume-title":"Curves and Surfaces for CAGD","author":"G. Farin","year":"1993","unstructured":"G. Farin, Curves and Surfaces for CAGD, 3rd ed. (Academic Press, Boston, 1993).","edition":"3rd ed."},{"key":"325394_CR5","doi-asserted-by":"publisher","first-page":"1553","DOI":"10.1090\/S0025-5718-96-00759-4","volume":"65","author":"R.T. Farouki","year":"1996","unstructured":"R.T. Farouki and T.N.T. Goodman, On the optimal stability of the Bernstein basis, Math. Comp. 65 (1996) 1553\u20131566.","journal-title":"Math. Comp."},{"key":"325394_CR6","unstructured":"R.T. Farouki, H.P. Moon and B. Ravani, Minkowski geometric algebra of complex sets, Geom. Dedicata (2000) to appear."},{"key":"325394_CR7","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/0167-8396(90)90023-K","volume":"7","author":"R.T. Farouki","year":"1990","unstructured":"R.T. Farouki and C.A. Neff, Analytic properties of plane offset curves & Algebraic properties of plane offset curves, Comput. Aided Geom. Design 7(1990) 83\u201399 & 101?127.","journal-title":"Comput. Aided Geom. Design"},{"key":"325394_CR8","doi-asserted-by":"publisher","first-page":"1589","DOI":"10.2307\/2153373","volume":"64","author":"R.T. Farouki","year":"1995","unstructured":"R.T. Farouki and C.A. Neff, Hermite interpolation by Pythagorean-hodograph quintics, Math. Comp. 64 (1995) 1589\u20131609.","journal-title":"Math. Comp."},{"key":"325394_CR9","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0167-8396(87)90012-4","volume":"4","author":"R.T. Farouki","year":"1987","unstructured":"R.T. Farouki and V.T. Rajan, On the numerical condition of polynomials in Bernstein form, Comput. Aided Geom. Design 4(1987) 191\u2013216.","journal-title":"Comput. Aided Geom. Design"},{"key":"325394_CR10","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/0734-189X(88)90123-5","volume":"44","author":"P.K. Ghosh","year":"1988","unstructured":"P.K. Ghosh, A mathematical model for shape description using Minkowski operators, Comput. Vision Graphics Image Process. 44 (1988) 239\u2013269.","journal-title":"Comput. Vision Graphics Image Process."},{"key":"325394_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-94702-5","volume-title":"Vorlesungen \u00fcber Inhalt, Oberfl\u00e4che, und Isoperimetrie","author":"H. Hadwiger","year":"1957","unstructured":"H. Hadwiger, Vorlesungen \u00fcber Inhalt, Oberfl\u00e4che, und Isoperimetrie (Springer, Berlin, 1957)."},{"key":"325394_CR12","unstructured":"A. Kaul, Computing Minkowski sums, Ph.D. thesis, Columbia University (1993)."},{"key":"325394_CR13","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1142\/S0218195995000258","volume":"5","author":"A. Kaul","year":"1995","unstructured":"A. Kaul and R.T. Farouki, Computing Minkowski sums of plane curves, Internat. J. Comput. Geom. Appl. 5 (1995) 413\u2013432.","journal-title":"Internat. J. Comput. Geom. Appl."},{"key":"325394_CR14","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1007\/BF01934076","volume":"21","author":"J.M. Lane","year":"1981","unstructured":"J.M. Lane and R.F. Riesenfeld, Bounds on a polynomial, BIT 21(1981) 112\u2013117.","journal-title":"BIT"},{"key":"325394_CR15","volume-title":"A Catalog of Special Plane Curves","author":"J.D. Lawrence","year":"1972","unstructured":"J.D. Lawrence, A Catalog of Special Plane Curves (Dover, New York, 1972)."},{"key":"325394_CR16","doi-asserted-by":"publisher","first-page":"136","DOI":"10.1006\/gmip.1998.0464","volume":"60","author":"I.K. Lee","year":"1998","unstructured":"I.K. Lee and M.S. Kim, Polynomial\/rational approximation of Minkowski sum boundary curves, Graphical Models Image Process. 60 (1998) 136\u2013165.","journal-title":"Graphical Models Image Process"},{"key":"325394_CR17","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/978-3-642-60607-6_7","volume-title":"Geometric Modeling: Theory and Practice","author":"I.K. Lee","year":"1997","unstructured":"I.K. Lee, M.S. Kim, and G. Elber, New approximation methods of planar offset and convolution curves, in: Geometric Modeling: Theory and Practice, eds. W. Strasser, R. Klein and R. Rau (Springer, Berlin, 1997) pp. 83\u2013101."},{"key":"325394_CR18","volume-title":"A Book of Curves","author":"E.H. Lockwood","year":"1967","unstructured":"E.H. Lockwood, A Book of Curves (Cambridge Univ. Press, Cambridge, 1967)."},{"key":"325394_CR19","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/BF01445180","volume":"57","author":"H. Minkowski","year":"1903","unstructured":"H. Minkowski, Volumen und Oberfl\u00e4che, Math. Ann. 57 (1903) 447\u2013495.","journal-title":"Math. Ann."},{"key":"325394_CR20","volume-title":"Interval Analysis","author":"R.E. Moore","year":"1966","unstructured":"R.E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1966)."},{"key":"325394_CR21","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970906","volume-title":"Methods and Applications of Interval Analysis","author":"R.E. Moore","year":"1979","unstructured":"R.E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, PA, 1979)."},{"key":"325394_CR22","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534471.001.0001","volume-title":"Visual Complex Analysis","author":"T. Needham","year":"1997","unstructured":"T. Needham, Visual Complex Analysis (Oxford Univ. Press, Oxford, 1997)."},{"key":"325394_CR23","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511526282","volume-title":"Convex Bodies: The Brunn-Minkowski Theory","author":"R. Schneider","year":"1993","unstructured":"R. Schneider, Convex Bodies: The Brunn-Minkowski Theory (Cambridge Univ. Press, Cambridge, 1993)."},{"key":"325394_CR24","volume-title":"Geometry of Complex Numbers","author":"H. Schwerdtfeger","year":"1979","unstructured":"H. Schwerdtfeger, Geometry of Complex Numbers (Dover, New York, 1979)."},{"key":"325394_CR25","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/S0010-4485(86)80013-6","volume":"18","author":"T.W. Sederberg","year":"1986","unstructured":"T.W. Sederberg and S.R. Parry, Comparison of three curve intersection algorithms, Comput. Aided Design 18 (1986) 58\u201364.","journal-title":"Comput. Aided Design"},{"key":"325394_CR26","volume-title":"Image Analysis and Mathematical Morphology","author":"J. Serra","year":"1982","unstructured":"J. Serra, Image Analysis and Mathematical Morphology (Academic Press, London, 1982)."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018910412112.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1018910412112\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1018910412112.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T23:17:14Z","timestamp":1747437434000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1018910412112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,7]]}},"alternative-id":["325394"],"URL":"https:\/\/doi.org\/10.1023\/a:1018910412112","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,7]]}}}