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The geometry of optimal degree reduction of Bezier curves

  • Optimal degree reductions, i.e. best approximations of \(n\)-th degree Bezier curves by Bezier curves of degree \(n\) - 1, with respect to different norms are studied. It is shown that for any \(L_p\)-norm the euclidean degree reduction where the norm is applied to the euclidean distance function of two curves is identical to componentwise degree reduction. The Bezier points of the degree reductions are found to lie on parallel lines through the Bezier points of any Taylor expansion of degree \(n\) - 1 of the original curve. This geometric situation is shown to hold also in the case of constrained degree reduction. The Bezier points of the degree reduction are explicitly given in the unconstrained case for \(p\) = 1 and \(p\) = 2 and in the constrained case for \(p\) = 2.

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Author:Guido Brunnett, Thomas Schreiber, Jörg Braun
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49109
Serie (Series number):Interner Bericht des Fachbereich Informatik (266)
Document Type:Report
Language of publication:English
Publication Date:2017/10/23
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/23
Number of page:15
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)