Share This Article:

Intersection Curves of Implicit and Parametric Surfaces in R3

Abstract Full-Text HTML Download Download as PDF (Size:282KB) PP. 1019-1026
DOI: 10.4236/am.2011.28141    5,309 Downloads   11,384 Views   Citations

ABSTRACT

We present algorithms for computing the differential geometry properties of Frenet apparatus {t,n,b,κ,τ} and higher-order derivatives of intersection curves of implicit and parametric surfaces in R3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Soliman, N. Abdel-All, S. Hassan and S. Badr, "Intersection Curves of Implicit and Parametric Surfaces in R3," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 1019-1026. doi: 10.4236/am.2011.28141.

References

[1] X. Ye and T. Maekawa, “Differential Geometry of Intersection Curves of Two Surfaces,” Computer-Aided Geometric Design, Vol. 16, No. 8, September 1999, pp. 767-788. doi:10.1016/S0167-8396(99)00018-7
[2] C. L. Bajaj, C. M. Hoffmann, J. E. Hopcroft and R. E. Lynch, “Tracing Surface Intersections,” Computer-Aided Geometric Design, Vol. 5, No. 4, November 1988, pp. 285-307. doi:10.1016/0167-8396(88)90010-6
[3] N. M. Patrikalakis, “Surface-to-Surface Intersection,” IEEE Computer Graphics & Applications, Vol. 13, No. 1, January-February 1993, pp. 89-95. doi:10.1109/38.180122
[4] T. J. Willmore, “An Introduction to Differential Geometry,” Clarendon Press, Oxford, 1959.
[5] M. Düldül, “On the Intersection Curve of Three Parametric Hypersurfaces,” Computer-Aided Geometric Design, Vol. 27, No. 1, January 2010, pp. 118-127. doi:10.1016/j.cagd.2009.10.002
[6] E. Kruppa, “Analytische und Konstruktive Differentialgeometrie,” Springer, Wien, 1957.
[7] E. Hartmann, “G2 Interpolation and Blending on Surfaces,” The Visual Computer, Vol. 12, No. 4, 1996, pp. 181-192. doi: 10.1007/s003710050057
[8] G. A. Kriezis, N. M. Patrikalakis and F.-E. Wolter, “Topological and Differential Equation Methods for Surface Intersections,” Computer-Aided Geometric Design, Vol. 24, No. 1, January 1992, pp. 41-55. doi:10.1016/0010-4485(92)90090-W
[9] R. C. Luo, Y. Ma and D. F. McAllister, “Tracing Tangential Surface-Surface Intersections,” Proceedings Third ACM Solid Modeling Symposium, Salt Lake City, 1995, pp. 255-262. doi:10.1145/218013.218070
[10] O. Aléssio, “Differential Geometry of Intersection Curves in of three Implicit Surfaces,” Computer-Aided Geometric Design, Vol. 26, No. 4, May 2009, pp. 455-471. doi:10.1016/j.cagd.2008.12.001
[11] M. P. do Carmo, “Differential Geometry of Curves and Surface,” Prentice Hall, Englewood Cliffs, NJ, 1976.
[12] J. J. Stoker, “Differential Geometry,” Wiley, New York, 1969.
[13] D. J. Struik, “Lectures on Classical Differential Geometry,” Addison-Wesley, Reading, 1950.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.