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105
Circular BernsteinBézier Polynomials
 Vanderbilt University Press (Nashville
, 1995
"... . We discuss a natural way to define barycentric coordinates associated with circular arcs. This leads to a theory of BernsteinB'ezier polynomials which parallels the familiar interval case, and which has close connections to trigonometric polynomials. x1. Introduction BernsteinB'ezier ..."
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Cited by 7 (5 self)
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. We discuss a natural way to define barycentric coordinates associated with circular arcs. This leads to a theory of BernsteinB'ezier polynomials which parallels the familiar interval case, and which has close connections to trigonometric polynomials. x1. Introduction Bernstein
BernsteinBézier Polynomials on Spheres and SphereLike Surfaces
 Comput. Aided Geom. Design
, 1996
"... In this paper we discuss a natural way to define barycentric coordinates on general spherelike surfaces. This leads to a theory of BernsteinBézier polynomials which parallels the familiar planar case. Our constructions are based on a study of homogeneous polynomials on trihedra in R³. The ..."
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Cited by 42 (11 self)
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In this paper we discuss a natural way to define barycentric coordinates on general spherelike surfaces. This leads to a theory of BernsteinBézier polynomials which parallels the familiar planar case. Our constructions are based on a study of homogeneous polynomials on trihedra in R³
JIANG: Fourier transform of BernsteinBézier polynomials
 J. Math. Anal. Appl
"... Explicit formulae, in terms of BernsteinBézier 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 ..."
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Cited by 2 (0 self)
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Explicit formulae, in terms of BernsteinBézier 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
On the Bernstein–Bézier form of Jacobi polynomials on a simplex
 J. Approx. Theory
, 2006
"... Here we give a simple proof of a new representation for orthogonal polynomials over triangular domains which overcomes the need to make symmetry destroying choices to obtain an orthogonal basis for polynomials of fixed degree by employing redundancy. A formula valid for simplices with Jacobi weights ..."
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Cited by 8 (3 self)
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weights is given, and we exhibit its symmetries by using the Bernstein–Bézier form. From it we obtain the matrix representing the orthogonal projection onto the space of orthogonal polynomials of fixed degree with respect to the Bernstein basis. The entries of this projection matrix are given explicitly
Limits of BernsteinBézier Curves for Periodic Control Nets
, 1992
"... : If n given control points b 0 ; . . . ; b n01 2 IR d are repeated periodically by b j+kn = b j for all k 2 ZZ, the uniform limit of the BernsteinB'ezier polynomial curves of degree r with control points b 0 ; . . . ; b r for r ! 1 is a Poisson curve (after a suitabl ..."
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: If n given control points b 0 ; . . . ; b n01 2 IR d are repeated periodically by b j+kn = b j for all k 2 ZZ, the uniform limit of the BernsteinB'ezier polynomial curves of degree r with control points b 0 ; . . . ; b r for r ! 1 is a Poisson curve (after a
A BERNSTEINBÉZIER BASIS FOR ARBITRARY ORDER RAVIARTTHOMAS FINITE ELEMENTS
"... Abstract. A BernsteinBézier basis is developed for H(div)conforming finite elements that gives a clear separation between the curls of the Bernstein basis for the polynomial discretisation of the space H 1, and the noncurls that characterize the specific H(div) finite element space (RaviartThoma ..."
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Abstract. A BernsteinBézier basis is developed for H(div)conforming finite elements that gives a clear separation between the curls of the Bernstein basis for the polynomial discretisation of the space H 1, and the noncurls that characterize the specific H(div) finite element space (Raviart
A bernsteinbézier based approach to soft tissue simulation
 Computer Graphics Forum
, 1998
"... This paper discusses a Finite Element approach for volumetric soft tissue modeling in the context of facial surgery simulation. We elaborate on the underlying physics and address some computational aspects of the finite element discretization. In contrast to existing approaches speed is not our firs ..."
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Cited by 24 (5 self)
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higher order interpolation functions using a BernsteinBézier formulation, which has various advantageous properties, such as its integral polynomial form of arbitrary degree, efficient subdivision schemes, and suitability for geometric modeling and rendering. In addition, the use of tetrahedral Finite
A bernsteinbezier sufficient condition for invertibility of polynomial mapping functions. Unpublished
, 2001
"... We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient condition is based on an analysis of the BernsteinBézier form of the columns of the derivati ..."
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Cited by 5 (1 self)
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We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient condition is based on an analysis of the BernsteinBézier form of the columns
Results 1  10
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105