Circular Approximation by Trigonometric Bézier Curves

Authors: Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa

Abstract:

We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

Keywords: Control points, rational trigonometric Bézier curves, radius error, shape measure, weight functions.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337928

References:

[1] L. Fang, “Circular arc approximation by quintic polynomial curves,”Computer Aided Geometric Design, vol. 15, 1998, pp. 843-861.
[2] M. Goldapp, “Approximation of circular arcs by cubic polynomials,”Computer Aided Geometric Design,vol. 8, 1991, pp. 227-238.
[3] X. Han, “Quadratic trigonometric polynomial curves with a shape parameter,”Computer Aided Geometric Design, vol. 19, 2002, pp. 503-512.
[4] X. Han, “Cubic trigonometric polynomial curves with a shape parameter,”Computer Aided Geometric Design, vol. 21, 2004, pp. 535-548.
[5] I. K. Lee, M. S. Kim and G. Elber, “Planer curve offset based on circular approximation,”Computer Aided Design,vol.28, no. 8, 1996, pp. 617-630.
[6] I. J. Schoenberg, “On trigonometric spline interpolation,”Journalof Mathematics and Mechanics,vol. 13, no. 5, 1964, pp. 795-825.
[7] G. Wang, Q. ChenandM. Zhou, “NUAT B-spline curves,”Computer Aided Geometric Design,vol. 21, 2004, pp. 193-205.