References
- C. de Boor and M. Sabin, High accuracy geometric Hermite interpolation, Comp. Aided Geom. Desi., 4 (1987), 269-278. https://doi.org/10.1016/0167-8396(87)90002-1
- K. Morken, Best approximation of circle segments by quadratic Bezier curves, Curves and Surfaces, Academic Press, (1990), 387-396.
- T. Dokken, M. Daehlen, T. Lyche, and K. Morken, Good approximation of circles by curvature-continuous Bezier curves, Comp. Aided Geom. Desi., 7 (1990), 33-41. https://doi.org/10.1016/0167-8396(90)90019-N
- M. Goldapp, Approximation of circular arcs by cubic polynomials, Comp. Aided Geom. Desi., 8 (1991), 227-238. https://doi.org/10.1016/0167-8396(91)90007-X
- T. Dokken, Controlling the shape of the error in cubic ellipse approximation, Curve and Surface Design, Saint-Malo, Nashboro Press (2002), 113-122.
- M. Floater, High-order approximation of conic sections by quadratic splines, Comp. Aided Geom. Desi., 12(6) (1995) 617-637. https://doi.org/10.1016/0167-8396(94)00037-S
-
M. Floater. An O(
$h^{2n}$ ) Hermite approximation for conic sections, Comp. Aided Geom. Desi., 14 (1997) 135-151. https://doi.org/10.1016/S0167-8396(96)00025-8 - T. Dokken. Aspects of intersection algorithms and approximation, PhD thesis, University of Oslo, (1997).
- Y. J. Ahn and H. O. Kim. Approximation of circular arcs by Bezier curves, J. Comp. Appl. Math., 81 (1997) 145-163. https://doi.org/10.1016/S0377-0427(97)00037-X
- L. Fang. Circular arc approximation by quintic polynomial curves, Comp. Aided Geom. Desi., 15 (1998), 843-861. https://doi.org/10.1016/S0167-8396(98)00019-3
- S. H. Kim and Y. J. Ahn. Approximation of circular arcs by quartic Bezier curves, Comp. Aided Desi., 39(6) (2007), 490-493. https://doi.org/10.1016/j.cad.2007.01.004
-
S. Hur and T. Kim. The best
$G^1$ cubic and$G^2$ quartic Bezier approximations of circular arcs, J. Comp. Appl. Math., 236 (2011), 1183-1192. https://doi.org/10.1016/j.cam.2011.08.002 - Z. Liu, J. Tan, X. Chen, and L. Zhang. An approximation method to circular arcs, Appl. Math. Comp., 15 (2012), 1306-1311.
-
S. W. Kim and Y. J. Ahn. Circle approximation by quartic
$G^2$ spline using alternation of error function, J. KSIAM, 17 (2013), 171-179. -
B. Kovac and E. Zagar. Some new
$G^1$ quartic parametric approximants of circular arcs, Appl. Math. Comp., 239 (2014), 254-264. https://doi.org/10.1016/j.amc.2014.04.100 - I.-K. Lee, M.-S. Kim, and G. Elber. Planar curve offset based on circle approximation, Comp. Aided Desi., 28 (1996), 617-630. https://doi.org/10.1016/0010-4485(95)00078-X
- G. Elber, I.-K. Lee, and M.-S. Kim. Comparing offset curve approximation methods, IEEE Comp. Grap. Appl., 17(3) (1997), 62-71. https://doi.org/10.1109/38.586019
- Y. J. Ahn, Y. S. Kim, and Y. Shin. Approximation of circular arcs and offset curves by Bezier curves of high degree, J. Comp. Appl. Math., 167 (2004), 405-416. https://doi.org/10.1016/j.cam.2003.10.008
- Y. J. Ahn, C. M. Hoffmann, and Y. S. Kim. Curvature-continuous offset approximation based on circle approximation using quadratic Bezier biarcs, Comp. Aided Desi., 43 (2011), 1011-1017. https://doi.org/10.1016/j.cad.2011.04.005
- Y. J. Ahn and C. M. Hoffmann. Circle approximation using LN Bezier curves of even degree and its application, J. Math. Anal. Appl., 40 (2014), 257-266.
-
W. Yang and X. Ye. Approximation of circular arcs by
$C^2$ cubic polynomial B-splines, 10th IEEE Intern. Conf. Comput.-Aided Des. Comput. Graph., (2007), 417-420. - B.-G. Lee, Y. Park, and J. Yoo. Application of Legendre-Bernstein basis transformations to degree elevation and degree reduction, Comp. Aided Geom. Desi., 19 (2002), 709-718. https://doi.org/10.1016/S0167-8396(02)00164-4
- H. Sunwoo. Matrix representation for multi-degree reduction of Bezier curves, Comp. Aided Geom. Desi., 22 (2005), 261-273. https://doi.org/10.1016/j.cagd.2004.12.002
- L. Piegl and W. Tiller. The NURBS book. Springer Science & Business Media, (2012).
- G. Farin. Curves and Surfaces for CAGD. Morgan-Kaufmann, San Francisco, (2002).
- W. Bohm. Inserting new knots into B-spline curves, Comp. Aided Desi., 4 (1980), 199-201.
- E. Cohen, T. Lyche, and R. Riesenfeld. Discrete B-splines and subdivision techniques in Computer-Aided Geometric Design and Computer Graphics, Comp. Grap. Image Proc., 14 (1980), 87-111. https://doi.org/10.1016/0146-664X(80)90040-4
- W. Bohm, G. Farin, and J. Kahmann. A survey of curve and surface methods in CAGD, Comp. Aided Geom. Desi., 1 (1984), 1-60. https://doi.org/10.1016/0167-8396(84)90003-7
- K. Morken, M. Reomers, and C. Schulz. Computing intersections of planar spline curves using knot insertion, Comp. Aided Geom. Desi., 26 (2009), 351-366. https://doi.org/10.1016/j.cagd.2008.07.005