Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31103
Computations of Bezier Geodesic-like Curves on Spheres

Authors: Sheng-Gwo Chen, Wen-Haw Chen


It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present by use of this method a computation of the Bezier geodesic-like curves on spheres.

Keywords: Geodesics, spheres, Bezier, Geodesic-like curve

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1326


[1] M.P. do Carmo, Differential geometry of curves and surfaces, prentice-Hall, Englewood Cliffs, NJ, 1976.
[2] S.-G. Chen, Geodesic-like curves on parametric surfaces, Computer Aided Geometric Design 27(1) (2010), pp106-117.
[3] I. Hotz and H. Hagen, Visualizing geodesics. In: Proceedings IEEE Visualization, Salt Lake City, UT (2000) pp. 311-318.
[4] Emin Kasap, Mustafa Yapici, F. Talay Akyildiz, 2005. A numerical study for computation of geodesic curves, Applied Mathematics and Computation, Volume 171, Issue 2, 1206-1213.
[5] Dimas Martinez, Luiz Velho. Paulo C. Carvalho, 2005. Computing geodesics on triangular meshes. Computer & Graphics, volume 29, 667-675.
[6] M. Paluszny, Cubic polynomial patches through geodesics. Computer-Aided Design 40 (2008), 56-61.
[7] K. Polthier and M. Schmies, 1998. In: Hege, H.C., Polthier, H.K. (Eds.), Straightest Geodesics On Polyhedral Surfaces in Mathematical Visualization. Springer-Verlag, Berlin.
[8] G.V.V. Ravi Kumar, K.G. Shastry, and B.G. Prakash, Computing offsets of trimmed NURBS surfaces. Computer-Aided Design 35 (2003a) 411-420.
[9] G.V.V. Ravi Kumar, P. Srinivasan, V. Devaraja Holla, K.G. Shastry and B.G. Prakash, 2003b. Geodesic curve computations on surfaces. Computer Aided Geometric Design 20 (2) (2003b), 119-133.
[10] J. Sanchez-Reyes and R. Dorado, Constrained design of polynomial surfaces from geodesic curves. CAD 40 (2008), 49-55.
[11] N. Sprynski, N. Szafran, B. Localle and L. Biard, Surface reconstruction via geodesic interpolation. CAD 40 (2008), 480-492.
[12] V. Surazhsky, T. Surazhsky, D. Kirsanov, S. Gortler and H. Hoppe, Fast exact and approximate geodesics on meshes. In: Proc. of SIGGRAPH 2005. ACM Transactions on Graphics 24 (3), 553-560.
[13] C.L. Tucker, 1997. Forming of advanced composites. In: Gutowski, T.G. (Ed.), Advanced Composites Manufacturing. Wiley, New York.