Based on a new developed recursive relation, a class of Quasi-Bernstein–Bézier polynomials over triangular domain with multiple shape parameters, which includes the classical Bernstein–Bézier ...polynomials and the cubic and quartic Said–Ball polynomials over triangular domain as special cases, is constructed. The given polynomials have some important and good properties for surface modeling, such as partition of unity, non-negativity, linear independence and so on. The shapes of the corresponding triangular Quasi-Bernstein–Bézier patch can be modified intuitively and foreseeable by altering the values of the shape parameters without changing the control points. In order to compute the patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the conditions for G1 continuous smooth joining two triangular Quasi-Bernstein–Bézier patches are derived.
Fourier transform of Bernstein–Bézier polynomials Chui, Charles K.; He, Tian-Xiao; Jiang, Qingtang
Journal of mathematical analysis and applications,
2007, 2007-01-00, Volume:
325, Issue:
1
Journal Article
Peer reviewed
Open access
Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. ...Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.
We present a local
C
1 spline interpolation scheme based on circular Bernstein–Bézier polynomials. The complexity of the spline can be significantly reduced by removing knots from the spline without ...perturbing the spline more than a given tolerance. We give the details of our approach and include some numerical examples.
In this article we present a computationally efficient subdivision algorithm for the evaluation of generalized Bernstein–Bézier curves. As particular cases we have subdivision algorithms for ...classical as well as trigonometric Bernstein–Bézier curves.
In this paper we present a new class of polynomial triangular macro-elements of arbitrary degree which are an extension of the classical Clough-Tocher cubic scheme. Their most important property is ...that the degree plays the role of a tension parameter, since these macro elements tend to the plane interpolating the vertices data. Graphical examples showing their use in scattered data interpolation are reported.
We propose a local method for the construction of differentiable functions which interpolate a set of gridded data and are monotonicity preserving, that is increasing or decreasing exactly where the ...data are. The scheme is based upon the boolean sum of cubic interpolating operators, which blend together shape-preserving, one dimensional, interpolating polynomials of adaptive degree. Error estimates are also provided.
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