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We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the polynomial Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.

We present a new approach to the problem of G k,l -constrained (k, l ≤ 3) multi-degree reduction of Bézier curves with respect to the least squares norm. First, to minimize the least squares error, we consider two methods of determining the values of geometric continuity parameters. One of them is based on quadratic and nonlinear programming, while the… (More)

We propose a novel approach to the problem of polynomial approximation of rational Bézier triangular patches with prescribed boundary control points. The method is very efficient thanks to using recursive properties of the bivariate dual Bernstein polynomials and applying a smart algorithm for evaluating a collection of two-dimensional integrals. Some… (More)

- Stanisław Lewanowicz, Gez, Wolfram Koepf
- 2007

Extending the results of [1] (see also [2]), we introduce the polynomials of the vector variable x ∈ R d , depending on two parameters q and ω, which generalize the classical multivariate Bernstein polynomials. For ω = 0, we obtain an extension of univariate q-Bernstein polynomials, recently introduced by Phillips [3]. Among the properties of the new… (More)

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