The de casteljau algorithm on SE(3)

2007 ◽  
pp. 23-34 ◽  
Author(s):  
Claudio Altafini
Keyword(s):  
De Casteljau Algorithm

scholarly journals A de Casteljau Algorithm for -Bernstein-Stancu Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Nowak
Keyword(s):  
Bernstein Polynomials ◽  
Classical Case ◽  
Geometric Progression ◽  
De Casteljau Algorithm ◽  
Stancu Operators

This paper is concerned with a generalization of the -Bernstein polynomials and Stancu operators, where the function is evaluated at intervals which are in geometric progression. It is shown that these polynomials can be generated by a de Casteljau algorithm, which is a generalization of that relating to the classical case and -Bernstein case.

Integer de Casteljau Algorithm for Rasterizing NURBS Curves

1992 ◽  
Vol 11 (2) ◽  
pp. 151-162 ◽  
Author(s):  
Narayanan Anantakrishnan ◽  
Les A. Piegl
Keyword(s):  
De Casteljau Algorithm ◽  
Nurbs Curves

Integration of Jacobi and Weighted Bernstein Polynomials Using Bases Transformations

2007 ◽  
Vol 7 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Abedallah Rababah
Keyword(s):  
Jacobi Polynomials ◽  
Bernstein Polynomials ◽  
Definite Integral ◽  
De Casteljau Algorithm ◽  
Bernstein Bases

AbstractThis paper presents methods to compute integrals of the Jacobi polynomials by the representation in terms of the Bernstein — B´ezier basis. We do this because the integration of the Bernstein — B´ezier form simply corresponds to applying the de Casteljau algorithm in an easy way. Formulas for the definite integral of the weighted Bernstein polynomials are also presented. Bases transformations are used. In this paper, the methods of integration enable us to gain from the properties of the Jacobi and Bernstein bases.

Rational Bézier Line-Symmetric Motions

1999 ◽  
Author(s):  
Shutian Li ◽  
Q. J. Ge
Keyword(s):  
Ruled Surface ◽  
Geometric Design ◽  
Ruled Surfaces ◽  
Line Geometry ◽  
Symmetric Motion ◽  
Computer Aided Geometric Design ◽  
De Casteljau Algorithm ◽  
Computer Aided ◽  
Kinematic Geometry

Abstract This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Bézier line-symmetric motions. By taking advantage of the kinematic geometry of a line-symmetric motion, the problem of synthesizing a rational Bézier line-symmetric motion is reduced to that of designing a rational Bézier ruled surface. In this way, a recently developed de Casteljau algorithm for line-geometric design of ruled surfaces can be applied. An example is presented in which the Bennet motion is represented as a rational Bézier line-symmetric motion whose basic surface is a hyperboloid.

scholarly journals Modification of the Curve and the Surface Polynomial Bezier Using de Casteljau Algorithm

CAUCHY ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 210
Author(s):  
Juhari Juhari
Keyword(s):  
Parametric Representation ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Parametric Surfaces ◽  
Shape Modification ◽  
De Casteljau Algorithm ◽  
Bézier Surfaces ◽  
Simulation Results ◽  
Bezier Surfaces ◽  
Design Objects

<p class="Abstract">Research carried out to obtain a Bezier curve of degree six resulting curvature of the curve is more varied and multifaceted. Stages in formulating applications Bezier surfaces revolution in design, there are three marble objects. First, calculate the parametric representation revolution Bezier surface and shape modification in a number of different forms. Second, formulate Bezier parametric surfaces that are continuously incorporated. Lastly, apply the formula to the design objects using computer simulation. Results marble obtained are Bezier curves of degree six modified version of the Bezier curve of degree five and some form of revolution Bezier surfaces are varied and multifaceted.</p>

scholarly journals Compensated de Casteljau algorithm in K times the working precision

2019 ◽  
Vol 357 ◽  
pp. 57-74
Author(s):  
Danny Hermes
Keyword(s):  
De Casteljau Algorithm

A de Casteljau algorithm for generalized Bernstein polynomials

1997 ◽  
Vol 37 (1) ◽  
pp. 232-236 ◽  
Author(s):  
George M. Phillips
Keyword(s):  
Bernstein Polynomials ◽  
De Casteljau Algorithm ◽  
Generalized Bernstein Polynomials
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