TY - RPRT
A1 - Brunnett, Guido
A1 - Schreiber, Thomas
A1 - Braun, Jörg
T1 - The geometry of optimal degree reduction of Bezier curves
N2 - 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.
T3 - Interner Bericht des Fachbereich Informatik - 266
Y1 - 1995
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4910
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-49109
ER -