1 |
A. Pallikaris and G. Latsas. New algorithm for great elliptic sailing (GES). J. Navi., 62:497-507, 2009.
|
2 |
T. Pavlidis. Curve fitting with conic splines. ACM Trans. Graph., 2:1-31, 1983.
DOI
|
3 |
A. F. Rasmussen and M. S. Floater. A point-based method for estimating surface area. In Proceedings of the SIAM Conference on Geometric Design, 2005.
|
4 |
J. A. Roulier. Specifying the arc length of Bezier curves. Comp. Aided Geom. Desi., 10:25-56, 1993.
DOI
ScienceOn
|
5 |
J. A. Roulier and B. Piper. Prescribing the length of parametric curves. Comp. Aided Geom. Desi., 13:3-22, 1996.
DOI
ScienceOn
|
6 |
J. A. Roulier and B. Piper. Prescribing the length of rational Bezier curves. Comp. Aided Geom. Desi., 13:23-42, 1996.
DOI
ScienceOn
|
7 |
M. Schechter. Which way is jerusalem? Navigating on a spheroid. The College Mathematics Journal, 38:96-105, 2007.
|
8 |
W.-K. Tseng and H.-S. Lee. Navigation on a great ellipse. J. Mari. Scie. Tech., 18:369-375, 2010.
|
9 |
H.Wang, J. Kearney, and K. Atkinson. Arc-length parametrized spline curves for real-time simulation. In Tom Lyche, Marie-Laurence Mazure, and Larry L. Schumaker, editors, Curve and Surface Design, pages 387-396, 2002.
|
10 |
M. S. Floater, A. F. Rasmussen, and U. Reif. Extrapolation methods for approximating arc length and surface area. Numer. Alg., 44:235-248, 2007.
DOI
ScienceOn
|
11 |
J. Gravesen. Adaptive subdivision and the length and energy of Bezier curves. Computational Geometry, 8:13-31, 1997.
DOI
ScienceOn
|
12 |
J. Gravesen. The arc-length and energy of rational Bezier curves. Mat-report 1997/26, Department of Mathematics, Technical University of Denmark, 1997.
|
13 |
E. T. Lee. The rational Bezier representation for conics. In geometric modeling : Algorithms and new trends, pages 3-19. SIAM, Academic Press, 1987.
|
14 |
G. Farin. Curves and Surfaces for Computer Aided Geometric Design. Morgan-Kaufmann, San Francisco, 2002.
|
15 |
J. Malczak. Quadratic Bezier curve length. Undated web page; http://segfaultlabs.com/docs/quadratic-bezier-curve-length, accessed 2010.
|
16 |
E. Boebert. Computing the arc length of cubic Bezier curves, 1993. http://steve.hollasch.net/cgindex/curves/cbezarclen.html, accessed 2010.
|
17 |
M. A. Earle. A vector solution for navigation on a great ellipse. J. Navi., 53:473-481, 2000.
DOI
ScienceOn
|
18 |
M. Floater. High-order approximation of conic sections by quadratic splines. Comp. Aided Geom. Desi., 12(6):617-637, 1995.
DOI
ScienceOn
|
19 |
M. Floater. An O() Hermite approximation for conic sectoins. Comp. Aided Geom. Desi., 14:135-151, 1997.
DOI
ScienceOn
|
20 |
M. S. Floater. Arc length estimation and the convergence of polynomial curve interpolation. Journal BIT Numerical Mathematics, 45:679-694, 2005.
DOI
|
21 |
M. S. Floater and A. F. Rasmussen. Point-based methods for estimating the length of a parametric curve. Journal of Computational and Applied Mathematics, 196:512-522, 2006.
DOI
ScienceOn
|
22 |
Y. J. Ahn. Conic approximation of planar curves. Comp. Aided Desi., 33:867-872, 2001.
DOI
ScienceOn
|
23 |
Y. J. Ahn. Helix approximation with conic and qadratic Bezier curves. Comp. Aided Geom. Desi., 22:551-565, 2005.
DOI
ScienceOn
|
24 |
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., 167:405-416, 2004.
DOI
ScienceOn
|
25 |
Y. J. Ahn. Approximation of conic sections by curvature continuous quartic Bezier curves. Comp. Math. Appl., 60:1986-1993, 2010.
DOI
ScienceOn
|
26 |
Y. J. Ahn and H. O. Kim. Curvatures of the quadratic rational Bezier curves. Comp. Math. Appl., 36:71-83, 1998.
|