Isometric transformations of the dual of the hexagonal lattice

Transformations of the used grid are basics of several algorithms of image processing and computer graphics. In this paper isometrical transformations on a hexagonal grid are provided, the vertices of the hexagonal grid are used in our grid as points. Simple transformations are widely used in square and cubic grids, where the space is described by independent coordinate values. Translations, rotations and mirror images of the grid are described mathematically using a symmetric coordinate system with 0 and 1 sum values.