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)


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


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


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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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