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Closed-form expressions for the approximation of arclength parameterization for Bézier curves

100%
Madi M.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 1
33-41
EN
In applications such as CNC machining, highway and railway design, manufacturing industry and animation, there is a need to systematically generate sets of reference points with prescribed arclengths along parametric curves, with sufficient accuracy and real-time performance. Thus, mechanisms to produce a parameter set that yields the coordinates of the reference points along the curve Q(t) = {x(t), y(t)} are sought. Arclength parameterizable expressions usually yield a parameter set that is necessary to generate reference points. However, for typical design curves, such expressions are not often available in closed form. It is thus desirable to find efficient ways to compensate for this lack of arclength parameterization. In this paper, several methods for approximating arclength parameterizations are studied. These methods are examined for both accuracy and real-time processing requirements. The application of generating reference points uniformly spaced along the paths of several curves is chosen for the illustration and comparison between the presented methods.
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A note on the rate of convergence for Chebyshev-Lobatto and Radau systems

88%
Berriochoa E., Cachafeiro A., Díaz J., Martínez E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
156-166
EN
This paper is devoted to Hermite interpolation with Chebyshev-Lobatto and Chebyshev-Radau nodal points. The aim of this piece of work is to establish the rate of convergence for some types of smooth functions. Although the rate of convergence is similar to that of Lagrange interpolation, taking into account the asymptotic constants that we obtain, the use of this method is justified and it is very suitable when we dispose of the appropriate information.
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