Fast algorithm for generating Bernstein-Bezier polynomials
نویسندگان
چکیده
منابع مشابه
Fast Algorithm for Composition of the Bernstein Polynomials
Composition of the Bernstein polynomials is an important research topic in computer-aided geometric design. This function is useful in implementing evaluation, subdivision, free-form deformation, trimming, conversion between tensor product and Bézier simplex forms, degree raising etc. To accomplish the composition, some numerically stable algorithms were introduced, such as blossoming algorithm...
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. Parametric curves are represented using these modified Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We get Bézier curve defined on [0, 1] when we set the parameter α, β to the value 0. We also present a de Casteljau algorithm to compute Bernstein Bézier curves and surfaces with shifted knots. The new curves have some properti...
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and Applied Analysis 3 for k 0, 1, . . . , n − j − 1 and fj f j / n . It is easily established by induction that qdifferences satisfy the relation Δqfj k ∑ i 0 −1 q i−1 /2 [ k i ] fj k−i. 1.10 In 2 , we prove that the operators B n f ;x defined by 1.4 can be expressed in terms of q-differences B q,α n f x n ∑ k 0 [ n k ] Δqf0 k−1 ∏ i 0 x α i 1 α i , 1.11 which generalized the well-known result ...
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In this paper, we use the blending functions of Lupaş type (rational) (p, q)-Bernstein operators based on (p, q)-integers for construction of Lupaş (p, q)-Bézier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupaş (p, q)-Bézier Bernstein functions. Parametric curves are represented using Lupaş (p...
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Fast algorithms for applying finite element mass and stiffness operators to the B-form of polynomials over d-dimensional simplices are derived. These rely on special properties of the Bernstein basis and lead to stiffness matrix algorithms with the same asymptotic complexity as tensor-product techniques in rectangular domains. First, special structure leading to fast application of mass matrice...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1994
ISSN: 0377-0427
DOI: 10.1016/0377-0427(92)00110-u