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Coplanar tricubes

  • Jean-Maurice Schramm
Discrete Shapes and Planes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)

Abstract

Within the framework of the arithmetic discrete geometry introduced by J.P.Reveillés, I. Debled has defined the concept of tricubes and found out that the total number of the tricubes that may appear in a naive plane is fourty.

This study concerns the coexistence of tricubes in a plane. We call complete combination of coplanar tricubes any set of tricubes, such as a naive plane exists, which contains all the tricubes of this set without any other. We present an algorithm which calculates the set of these combinations.

It appears that the number of these combinations is quite small : only 99, although a “combinatory explosion” could have been expected during their calculation. Their list is given in the appendix.

Key words

arithmetic discrete geometry discrete planes Fourier's algorithm 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jean-Maurice Schramm
    • 1
  1. 1.Laboratoire des Sciences de l'Image, d'Informatique et de TélédétectionStrasbourg cedexFrance

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