Parametric Rational Cubic Approximation Scheme for Circular Arcs

被引：0

作者：

Shakeel A. ^{[1
]}

Hussain M. ^{[2
]}

Hussain M.Z. ^{[3
]}

机构：

[1] Faculty of Science and Technology, University of Central Punjab, Lahore

[2] Lahore College for Women University, Lahore

[3] Department of Mathematics, University of the Punjab, Lahore

来源：

International Journal of Applied and Computational Mathematics | 2024年 / 10卷 / 2期

关键词：

65D05; 65D07; 65D18; 68U05; Absolute radius error; Circular arcs; G[!sup]2[!/sup]-constraints; Parametric rational cubic function;

D O I：

10.1007/s40819-023-01630-3

中图分类号：

学科分类号：

摘要：

The research paper presents a numerical method for the G2- approximation of circular arcs. The developed technique is worked on a quarter circle and the complete circle is formed using affine transformation. The optimal value of the free parameters is searched by reducing the approximation error to its minimum. Approximation order of the proposed scheme varies from Oγ2 to Oγ4, depending on the choice of free parameters. The proposed approximation scheme has an improved level of accuracy than the prevailing schemes. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

引用

共 20 条

[11]

Jahanshahloo A., Ebrahimi A., Reconstruction of the initial curve from a two-dimensional shape for the B-spline curve fitting, Eur. Phys. J. Plus, 137, 3, (2022)

[12]

Jahanshahloo A., Ebrahimi A., Reconstruction of 3D shapes with B-spline surface using diagonal approximation BFGS methods, Multimed. Tools Appl, 81, pp. 38091-38111, (2022)

[13]

Kim S., Ahn Y.J., An approximation of circular arcs by quartic Bézier curves, Comput. Aided Des, 39, pp. 490-493, (2007)

[14]

Kim S.W., Ahn Y.J., Circle approximation by quartic G<sup>2</sup> spline using alternation of error function, J. Korean Soc. Ind. Appl. Math, 17, 3, pp. 171-179, (2013)

[15]

Lewanowicz S., Wozny P., Bézier representation of constrained dual Bernstein polynomials, Appl. Math. Comput, 218, 8, pp. 4580-4586, (2011)

[16]

Lin J., Ball A.A., Zheng J.J., Approximating circular arcs by Bézier curves and its application to modeling tooling for FE forming simulations, Int. J. Mach. Tools Manuf, 41, pp. 703-717, (2001)

[17]

Liu Z., Tan J., Chen X., Zhang L., An approximation method to circular arcs, Appl. Math. Comput, 219, pp. 1306-1311, (2012)

[18]

Marsh D., Applied Geometry for Computer Graphics and CAD, (2005)

[19]

Ribeiro L.L.S., Ranga A.S., A modified least squares method: approximations on the unit circle and on (-1, 1), J. Comput. Appl. Math, 410, pp. 114-168, (2022)

[20]

Sarfraz M., Hussain M.Z., Hussain M., Modeling rational spline for visualization of shaped data, J. Numer. Math, 21, 1, pp. 63-87, (2013)

← 1 2 →