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A Mathematica Package for Computing and Visualizing the Gauss Map of Surfaces

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Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3482))

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Abstract

One of the most interesting and striking concepts in Differential Geometry is that of the Gauss map. In the case of surfaces, this map projects surface normals to a unit sphere. This strategy is especially useful when analyzing the shape structure of a smooth surface. This paper describes a new Mathematica package, GaussMap, for computing and displaying the tangent and normal vector fields and the Gauss map of surfaces described symbolically in either implicit or parametric form. The performance of the package is discussed by means of several illustrative and interesting examples. The package presented here can be applied for visualizing and studying the geometry of a surface under analysis, thus providing the users with an excellent computer tool for teaching and visualization purposes.

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References

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

    MATH  Google Scholar 

  2. Koenderink, J.J.: Solid Shape. MIT Press, Cambridge (1990)

    Google Scholar 

  3. Lowekamp, B., Rheingans, P., Yoo, T.S.: Exploring Surface Characteristics with Interactive Gaussian Images (A Case Study). In: Proceedings of IEEE Visualization 2002, pp. 553–556. IEEE Computer Society Press, Los Alamitos (2002)

    Chapter  Google Scholar 

  4. Maeder, R.: Programming in Mathematica, 2nd edn. Addison-Wesley, Redwood City (1991)

    Google Scholar 

  5. O’Neill, B.: Elementary Differential Geometry, 2nd edn. Academic Press, San Diego (1997)

    MATH  Google Scholar 

  6. Tanaka, H.T., Ikeda, M., Chiaki, H.: Automatic face and gesture recognition. In: Proceedings of the 15th International Conference on Pattern Recognition 2000, pp. 372–377. IEEE Computer Society Press, Los Alamitos (1998)

    Google Scholar 

  7. Wolfram, S.: The Mathematica Book, 4th edn. Wolfram Media, Champaign, IL & Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Piura, Urb. Miraflores s/n, Castilla, Piura, Perú

    R. Ipanaqué

  2. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, E-39005, Santander, Spain

    A. Iglesias

  3. Laboratory of Advanced Research, University of Tsukuba, Tsukuba, Japan

    A. Iglesias

Authors
  1. R. Ipanaqué
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  2. A. Iglesias
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering, Department University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganà

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Ipanaqué, R., Iglesias, A. (2005). A Mathematica Package for Computing and Visualizing the Gauss Map of Surfaces. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_52

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  • DOI: https://doi.org/10.1007/11424857_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25862-9

  • Online ISBN: 978-3-540-32045-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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