A note on iterative process for G
            2-multi degree reduction of Bézier curves

A note on iterative process for G 2-multi degree reduction of Bézier curves

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Article ID: iaor20121893
Volume: 218
Issue: 12
Start Page Number: 6987
End Page Number: 6990
Publication Date: Feb 2012
Journal: Applied Mathematics and Computation
Authors:
Keywords: graphs, programming: convex, programming: quadratic
Abstract:

In the paper [A. Rababah, S. Mann, Iterative process for G 2‐multi degree reduction of Bézier curves, Applied Mathematics and Computation 217 (2011) 8126–8133], Rababah and Mann proposed an iterative method for multi‐degree reduction of Bézier curves with C 1 and G 2‐continuity at the endpoints. In this paper, we provide a theoretical proof for the existence of the unique solution in the first step of the iterative process, while the proof in their paper applies only in some special cases. Also, we give a complete convergence proof for the iterative method. We solve the problem by using convex quadratic optimization.

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