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A digital geometry for hexagonal pixels
Image and Vision Computing, 1989Abstract Comparison of hexagonal and square pixels and arrays for image processing shows that the former have many advantages. However, squares can be addressed with integers and orthogonal axes, while for hexagons the axes must be at an oblique angle of 60°. This paper describes a general method of producing geometrical algorithms for such axes.
Sarah BM Bell +2 more
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Inter-diagrammatic Reasoning and Digital Geometry
2004In this paper we examine inter-diagrammatic reasoning (IDR) as a framework for digital geometry. We show how IDR can be used to represent digital geometry in two dimensions, as well as providing a concise language for specifying algorithms. As an example, we specify algorithms and examine the algorithmic complexity of using IDR for reasoning about the ...
Robert McCartney, Passent El-Kafrawy
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Counting minimal paths in digital geometry
Pattern Recognition Letters, 1991Abstract In this paper recursive formulae are derived for determining the number of the minimal cityblock, chessboard or octagonal paths in the two-dimensional digital plane.
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Generalized triangular grids in digital geometry
2004Summary: 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 one- and two-plane triangular grids). This family comes from mapping their points to \(Z^3\). Their symmetric properties are triangular.
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A New Concept for Digital Geometry
1994A concept for geometry in a topological space with finitely many elements without the use of infinitesimals is presented. The notions of congruence, collinearity, convexity, digital lines, perimeter, area, volume, etc. are defined. The classical notion of continuous mappings is transferred (without changes) onto finite spaces.
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