New Approach to Approximate Circular Arc by Quartic Bezier Curve

Affiliation(s)

Nor’ashiqin Mohd Idrus Department of Mathematics Universiti Pendidikan Sultan Idris Tanjung Malim, Perak, Malaysia.

School of Mathematical Science Universiti Sains Malaysia Penang, Malaysia.

Nor’ashiqin Mohd Idrus Department of Mathematics Universiti Pendidikan Sultan Idris Tanjung Malim, Perak, Malaysia.

School of Mathematical Science Universiti Sains Malaysia Penang, Malaysia.

ABSTRACT

This paper presents a result of approximation an arc circles by using a quartic Bezier curve. Based on the barycentric coordinates of two and three combination of control points, the interior control points are determined by forcing the curvature at median point as similar as the given curvature at end points. Hausdorff distance is used to investigate the order of accuracy compare to the actual arc circles through central angle of . We found that the optimal approximation order is eight which is somewhat similar to preceding methods in the literatures.

This paper presents a result of approximation an arc circles by using a quartic Bezier curve. Based on the barycentric coordinates of two and three combination of control points, the interior control points are determined by forcing the curvature at median point as similar as the given curvature at end points. Hausdorff distance is used to investigate the order of accuracy compare to the actual arc circles through central angle of . We found that the optimal approximation order is eight which is somewhat similar to preceding methods in the literatures.

Cite this paper

nullAhmad, A. , Masri, R. and Ali, J. (2012) New Approach to Approximate Circular Arc by Quartic Bezier Curve.*Open Journal of Applied Sciences*, **2**, 132-737. doi: 10.4236/ojapps.2012.24B032.

nullAhmad, A. , Masri, R. and Ali, J. (2012) New Approach to Approximate Circular Arc by Quartic Bezier Curve.

References

[1] Ahn Y.J. and Kim H.O. Approximation of circular arcs by Bezier curves. Computer Aided Geometric Design, 81:145-163, 1997.

[2] deBoor C., Hollig K. and Sabin M. High accuracy geometric Hermite interpolation. Computer Aided Geometric Design, 4:269–278, 1987.

[3] Dokken T. , Dehlen M., Lyche T and Morken K. Good approximation of circles by curvature-continuous Bezier curves. Computer Aided Geometric Design, 7:33-41, 1990.

[4] Fang L. Circular arc approximation by quintic polynomial curves. Computer Aided Geometric Design, 15:843-861, 1998.

[5] Goldapp M., Approximation of circular arcs by cubic polynomial. Computer Aided Geometric Design, 3:227-238, 1991

[6] Grandine T.A and Hogan T.A. A parametric quartic spline interpolant to position, tangent and curvature. Computing (DOI), 72:65-78, 2004.

[7] Kim S.H. and Ahn Y.J. An approximation of circular arcs by quartic Bezier curves. Computer Aided Geometric Design, 30:490-493, 2007.

[8] Riskus A. Approximation of a cubic Bezier curve by circular arcs and vice versa. Information Technology and control, Vol 35, 4:371-378, 2006.

[9] Yamaguchi F. Curves and surfaces in computer aided geometric design. Springer-Verlag 1988

[10] ?agar, Emil, Jakli?, Ga?per, Kozak, Jernej, Krajnc, Marjeta. Approximation of circular arcs by parametric polynomial curves . Annali Dell'Universita' di Ferrara, 53;2:271-279, 2007.

[1] Ahn Y.J. and Kim H.O. Approximation of circular arcs by Bezier curves. Computer Aided Geometric Design, 81:145-163, 1997.

[2] deBoor C., Hollig K. and Sabin M. High accuracy geometric Hermite interpolation. Computer Aided Geometric Design, 4:269–278, 1987.

[3] Dokken T. , Dehlen M., Lyche T and Morken K. Good approximation of circles by curvature-continuous Bezier curves. Computer Aided Geometric Design, 7:33-41, 1990.

[4] Fang L. Circular arc approximation by quintic polynomial curves. Computer Aided Geometric Design, 15:843-861, 1998.

[5] Goldapp M., Approximation of circular arcs by cubic polynomial. Computer Aided Geometric Design, 3:227-238, 1991

[6] Grandine T.A and Hogan T.A. A parametric quartic spline interpolant to position, tangent and curvature. Computing (DOI), 72:65-78, 2004.

[7] Kim S.H. and Ahn Y.J. An approximation of circular arcs by quartic Bezier curves. Computer Aided Geometric Design, 30:490-493, 2007.

[8] Riskus A. Approximation of a cubic Bezier curve by circular arcs and vice versa. Information Technology and control, Vol 35, 4:371-378, 2006.

[9] Yamaguchi F. Curves and surfaces in computer aided geometric design. Springer-Verlag 1988

[10] ?agar, Emil, Jakli?, Ga?per, Kozak, Jernej, Krajnc, Marjeta. Approximation of circular arcs by parametric polynomial curves . Annali Dell'Universita' di Ferrara, 53;2:271-279, 2007.