We study the relationship of transformations between Legendre and Bernstein basis. Using the relationship, we present a simple and efficient method for optimal multiple degree reductions of Bézier curves with respect to the L 2 -norm.
In this article, we find the optimal r times degree reduction of Bézier curves with respect to the Jacobi-weighted L 2 -norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L 1 , L 2 , and L ∞ -norms. We give some examples and figures to demonstrate these methods.
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