Acta Mathematica Hungarica

, Volume 156, Issue 1, pp 182–193 | Cite as

Uniform refinable 3D grids of regular convex polyhedrons and balls

  • A. Holhoş
  • D. Roşca


We construct a simple volume-preserving map from the cube [0,b]3 to the tetrahedron \({\{(x,y,z)\in \mathbb R^3}\), \({x \geq0}\), \({y \geq 0}\), \({z \geq 0}\), \({x+y+z\leq a\},}\) with \({a=b\sqrt[3]6}\). This map will allow us to construct equal-volume subdivisions of arbitrary tetrahedrons and arbitrary convex polyhedrons into polyhedral cells. Moreover, mapping the regular octahedron onto the ball using a volume-preserving map previously constructed by the authors, one can obtain uniform and refinable grids on the 3D ball by a simple procedure, starting from appropriate grids on the cube.

Mathematics Subject Classification

52B70 65N55 

Key words and phrases

equal volume projection uniform spherical grid hierarchical grid 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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