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Sphere Construction on the FCC Grid Interpreted as Layered Hexagonal Grids in 3D

  • Girish Koshti
  • Ranita BiswasEmail author
  • Gaëlle Largeteau-Skapin
  • Rita Zrour
  • Eric Andres
  • Partha Bhowmick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11255)

Abstract

In this paper, we propose an algorithm to build discrete spherical shell having integer center and real-valued inner and outer radii on the face-centered cubic (FCC) grid. We address the problem by mapping it to a 2D scenario and building the shell layer by layer on hexagonal grids with additive manufacturing in mind. The layered hexagonal grids get shifted according to need as we move from one layer to another and forms the FCC grid in 3D. However, we restrict our computation strictly to 2D in order to utilize symmetry and simplicity.

Keywords

Discrete sphere Hexagonal grid Face-centered cubic grid Digital geometry Additive manufacturing 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Girish Koshti
    • 1
  • Ranita Biswas
    • 1
    Email author
  • Gaëlle Largeteau-Skapin
    • 2
  • Rita Zrour
    • 2
  • Eric Andres
    • 2
  • Partha Bhowmick
    • 3
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.University of Poitiers, Laboratory XLIM, ASALI, UMR CNRS 7252Futuroscope ChasseneuilFrance
  3. 3.Department of Computer Science and EngineeringIndian Institute of Technology KharagpurKharagpurIndia

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