The best quintic chebyshev approximation of circular arcs of order ten

Abedallah Rababah

doi:10.11591/ijece.v9i5.pp3779-3785

The best quintic chebyshev approximation of circular arcs of order ten

Abedallah Rababah

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree 10 rather than 6; the Chebyshev error function equioscillates 11 times rather than 7; the approximation order is 10 rather than 6. The method approximates more than the full circle with Chebyshev uniform error of 1/2⁹. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.

Original language	English
Pages (from-to)	3779-3785
Number of pages	7
Journal	International Journal of Electrical and Computer Engineering
Volume	9
Issue number	5
DOIs	https://doi.org/10.11591/ijece.v9i5.pp3779-3785
Publication status	Published - Oct 2019
Externally published	Yes

Keywords

Approximation order
Bézier curves
CAD
Circular arc
High accuracy
High performance computing
Quintic approximation

ASJC Scopus subject areas

General Computer Science
Electrical and Electronic Engineering

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10.11591/ijece.v9i5.pp3779-3785

Cite this

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title = "The best quintic chebyshev approximation of circular arcs of order ten",

abstract = "Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree 10 rather than 6; the Chebyshev error function equioscillates 11 times rather than 7; the approximation order is 10 rather than 6. The method approximates more than the full circle with Chebyshev uniform error of 1/29. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.",

keywords = "Approximation order, B{\'e}zier curves, CAD, Circular arc, High accuracy, High performance computing, Quintic approximation",

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AU - Rababah, Abedallah

PY - 2019/10

Y1 - 2019/10

N2 - Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree 10 rather than 6; the Chebyshev error function equioscillates 11 times rather than 7; the approximation order is 10 rather than 6. The method approximates more than the full circle with Chebyshev uniform error of 1/29. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.

AB - Mathematically, circles are represented by trigonometric parametric equations and implicit equations. Both forms are not proper for computer applications and CAD systems. In this paper, a quintic polynomial approximation for a circular arc is presented. This approximation is set so that the error function is of degree 10 rather than 6; the Chebyshev error function equioscillates 11 times rather than 7; the approximation order is 10 rather than 6. The method approximates more than the full circle with Chebyshev uniform error of 1/29. The examples show the competence and simplicity of the proposed approximation, and that it can not be improved.

KW - Approximation order

KW - Bézier curves

KW - CAD

KW - Circular arc

KW - High accuracy

KW - High performance computing

KW - Quintic approximation

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JO - International Journal of Electrical and Computer Engineering

JF - International Journal of Electrical and Computer Engineering

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ER -

The best quintic chebyshev approximation of circular arcs of order ten

Abstract

Keywords

ASJC Scopus subject areas

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