**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Improvement of the Shortest Path Problem with Geodesic-Like Method

**Authors:**
Wen-Haw Chen

**Abstract:**

**Keywords:**
shortest paths,
geodesic-like method,
NURBS surfaces.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1329725

**References:**

[1] M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice- Hall, Englewood Cliffs, NJ. (1976).

[2] V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours, Int. J. Comput. Vision 22 (1) (1997) 61-71.

[3] X. D. Chen, H. Su, J. H. Yong, J. C. Paul and J. G. Sun, A counterexample on point inversion and projection for NURBS curve, CAGD 24 (2007) 302.

[4] X.-D. Chen, J.-H. Yong, Guozhao Wang, J.-C. Paul and Gang Xu, Computing the minimum distance between a point and a NURBS curve, CAD 40 (2008) 1051-1054.

[5] X.-D. Chena, J.-H. Yonga, G.-Q. Zhenga, J.-C. Paula and J.-G. Suna, Computing minimum distance between two implicit algebraic surfaces, CAD 38 (2006) 1053-1061.

[6] S.-G. Chen, Geodesic-like curves on parametric surfaces, CAGD 27 (2010) 106-117.

[7] S.-G. Chen and W.-H. Chen, Computation of Shortest Paths Between Two Curves on Surfaces by Geodesic-Like Algorithm, preprint.

[8] J. M. Gutierrez and M. A. Hernandez, An acceleration of Newton-s method: Super- Halley method, Applied Mathematics and Computation 117(2) (2001) 223-239.

[9] I. Hotz and H. Hagen, Visualizing geodesics, In: Proceedings IEEE Visualization (Salt Lake City, UT,2000) pp. 311-318.

[10] S. M. Hu and J. Wallner, A second order algorithm for orthogonal projection onto curves and surfaces, CAGD 22(3) (2005) 251-60.

[11] T. Kanai and H. Suzuki, Approxmiate shortest path on a polyhedral surface and its applications, CAD 33 (2001) 801-811

[12] E. Kasap, M. Yapici and F. T. Akyildiz, A numerical study for computation of geodesic curves, Applied Mathematics and Computation 171(2) (2005) 1206-1213.

[13] K.-J. Kim, Minimum distance between a canal surface and a simple surface, CAD 35 (2003) 871-879.

[14] R. Kimmel, Intrinsic scale space for images on surfaces: the geodesic curvature flow, Graph. Models Image Process 59(5) (1997) 365-372.

[15] D. Martinez, L. Velho and P. C. Carvalho, Computing geodesics on triangular meshes, Computer & Graphics 29 (2005) 667-675.

[16] Y. L. Ma and W. T. Hewitt, Point inversion and projection for NURBS curve and surface: Control polygon approach, CAGD 20(2) (2003) 79-99.

[17] T. Maekawa, Computation of shortest path on free-form parametric surfaces, Journal of Mechanical Design, Transactions of ASME, 118(4) (1996) 499-508.

[18] N. Patrikalakis, T. Maekawa, Shape interrogation for computer aided design and manufacturing, Springer; 2001.

[19] L. Piegl and W. Tiller, Parametrization for surface fitting in reverse engineering, CAD 33(8) (2001) 593-603.

[20] J. Pegna and F. E. Wolter, Surface curve design by orthogonal projection of space curves onto free-form surfaces, Journal of Mechanical Design, ASME Transactions 118(1) (1996) 45-52.

[21] E. Polak, Optimization, algorithms and consistent approximations, Berlin (Heidelberg, NY): Springer-Verlag; 1997.

[22] K. Polthier, M. Schmies, 1998. In: Hege, H.C., Polthier, H.K. (Eds.), Straightest Geodesics On Polyhedral Surfaces in Mathematical Visualization, Springer-Verlag, Berlin.

[23] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C: The art of scientific computing, 2nd ed.NewYork: Cambridge University Press, 1992.

[24] G. V. V. Ravi Kumar, Prabha Srinivasan, V. Devaraja Holla, K. G. Shastry and B. G. Prakash, Geodesic curve computations on surfaces, CAGD 20(2) (2003) 119-133.

[25] J. S'anchez-Reyesa and R. Doradob, Constrained design of polynomial surfaces from geodesic curves, CAD 40 (2008) 49-55.

[26] I. Selimovic, Improved algorithms for the projection of points on NURBS curves and surfaces, CAGD 23(5) (2006) 439-445.

[27] V. Surazhsky, T. Surazhsky, D. Kirsanov, S. Gortler, H. Hoppe, Fast exact and approximate geodesics on meshes, ACM Transactions on Graphics (Proc. of SIGGRAPH 2005), 24(3), 553-560.

[28] Y. Ye, Combining binary search and Newton-s method to compute real roots for a class of real functions, Journal of Complexity 10(3) (1994) 271-280.