Graceful Planes and Thin Tunnel-Free Meshes

  • Valentin E. Brimkov
  • Reneta P. Barneva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

In this paper we present an approach to describe polyhedra by meshes of discrete triangles. The study is based on the theory of arithmetic geometry [10]. We introduce a new class of discrete planes (respectively lines) which we call graceful planes (respectively graceful lines).We use naive planes and graceful lines to obtain as thin as possible triangular mesh discretization admitting an analytical description. The interiors of the triangles are portions of naive planes, while the sides are graceful lines

Keywords

Discrete 3D modeling Discrete planes Discrete lines Discrete triangles Mesh of triangles 

References

  1. 1.
    Andres, E., Acharya, R., Sibata, C.: Discrete Analytical Hyperplanes. GMIP59 (1997) 302–309Google Scholar
  2. 2.
    Andres, E., Jacob, M.-A.: The Discrete Analytical Hyperspheres. IEEE TVCG3 (1997) 75–86Google Scholar
  3. 3.
    Andres, E., Nehlig, Ph., Françon, J.: Supercover of Straight Lines, Planes, and Triangles. In: Ahronovitz, E., Fiorio, Ch. (eds.): Discrete Geometry for Computer Imagery. Springer-Verlag, Berlin Heidelberg New York (1996) 243–254Google Scholar
  4. 4.
    Bresenham, J.E.: Algorithm for Computer Control of a Digital Plotter. ACM Trans. on Graphics4 (1965) 25–30Google Scholar
  5. 5.
    Barneva, R.P., Brimkov, V.E., Nehlig, Ph.: Thin Discrete Triangular Meshes. Tech. Rep. RR 98/01, LSIIT, Strasbourg (1998). To appear in Theor. Comp. Sc. (Elsevier)Google Scholar
  6. 6.
    Debled-Renesson, I.: Reconnaissance des Droites et Plans Discrets. Thèse de doctorat, Université Louis Pasteur, Strasbourg (1995)Google Scholar
  7. 7.
    Debled-Renesson, I., Reveillès, J.-P.: A New Approach to Digital Planes. In: Spie’s International Symposium on Photonics for Industrial Applications, Technical Conference Vision Geometry 3, Boston (1994)Google Scholar
  8. 8.
    Figueiredo, O., Reveillès, J.-P.: A Contribution to 3D Digital Lines. In: Discrete Geometry for Computer Imagery, 5th Int.Workshop, Clermont-Ferrand (1995) 187–198Google Scholar
  9. 9.
    Françon J.: On Recent Trends in Discrete Geometry in Computer Imagery. In: Miguet, S., Montanvert, A., Ubeda, S. (eds.): Discrete Geometry for Computer Imagery. Lecture Notes in Computer Sciences, Vol. 1176. Springer-Verlag, Berlin Heidelberg New York (1996) 141–150Google Scholar
  10. 10.
    Reveillès, J.-P.: Géométrie Discréte, Calcul en Nombres Entiers et Algorithmique. Thèse d’état, Universitè Louis Pasteur, Strasbourg (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Valentin E. Brimkov
    • 1
  • Reneta P. Barneva
    • 1
  1. 1.Eastern Mediterranean UniversityFamagustaTurkey

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