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Applied Mathematics Research eXpress (2005) Vol. 2005 : article ID 169, 182 pages, doi:10.1155/AMRX.2005.169
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Copyright © 2005 Hindawi Publishing Corporation. All rights reserved.

On a modified Durrmeyer-Bernstein operator and applications

Germain E. Randriambelosoa

We present two applications of a modified Durrmeyer-Bernsteinoperator introduced by Goodman and Sharma. A new method isproposed achieving a "good" degree reduction of a Béziercurve with endpoint interpolation. A convenient algorithm will begiven providing an easy and practical method for computing thedegree reduced curve. Then, given a set of (r+1) points, weconstruct a degree n Bézier curve approximation within adistance O(n–1/2) from the given points, where n does notdepend on r.


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