Generalised triangular grids in digital geometry

Nagy, Benedek (2004) Generalised triangular grids in digital geometry. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 20 (1). pp. 63-78. ISSN 0866-0174

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Abstract

The hexagonal and the triangular grids are duals of each other. These two grids are the first and second ones in the family of triangular grids (we can call them as one- and two-planes triangular grids). This family comes from the mapping their points to ℤ3. Their symmetric properties are triangular. The next grid is the three-planes triangular grid, which looks like the mix of them. In this paper we analyze this grid and its dual from view of neighbouring conditions. After this we consider the n-planes grid. We prove that for n > 3 the n-planes triangular grids are non-planar. We also examine the 'circular' three-planes grid and the higher dimensional triangular grids.

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