Subharmonicity and convexity properties of Bernstein polynomials and Bézier nets on triangles
نویسندگان
چکیده
This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order to better compare these properties, the different notations used by different authors are unified. It also includes counterexamples for the results that are not true. 1999 Elsevier Science B.V. All rights reserved.
منابع مشابه
Linear convexity conditions for rectangular and triangular Bernstein-Bézier surfaces
The goal of this paper is to derive linear convexity conditions for Bernstein–Bézier surfaces defined on rectangles and triangles. Previously known linear conditions are improved on, in the sense that the new conditions are weaker. Geometric interpretations are provided.
متن کاملTensor-product monotonicity preservation
The preservation of surface shape is important in geometric modelling and approximation theory. In geometric modelling one would like to manipulate the shape of the surface being modelled by the simpler task of manipulating the control points. In scattered data approximation one might wish to approximate bivariate data sampled from a function with a shape property by a spline function sharing t...
متن کاملThe Genuine Bernstein{Durrmeyer Operator on a Simplex
In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...
متن کاملOn convex Bézier triangles
— Goodman [8] showed that uniform subdivision of triangular Bézier nets preserves convexity. Hère, a very short proofofthis f act is given which applies even to box spline surfaces and degree élévation instead of subdivision. Secondiy, it is shown that every Bézier net of a quadratic convex Bézier triangle can be subdivided such that the net becomes convex.
متن کاملOn a generalization of Bernstein polynomials and Bézier curves based on umbral calculus
In [20] a generalization of Bernstein polynomials and Bézier curves based on umbral calculus has been introduced. In the present paper we describe new geometric and algorithmic properties of this generalization including: (1) families of polynomials introduced by Stancu [19] and Goldman [12], i.e., families that include both Bernstein and Lagrange polynomial, are generalized in a new way, (2) a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Computer Aided Geometric Design
دوره 16 شماره
صفحات -
تاریخ انتشار 1999