On the Size of the Bijective Regions in Digital Rotations on the Hexagonal Grid

Abstract

In this paper, we consider the digital rotations on the hexagonal and triangular grids, where the center of rotation is the midpoint of a given main pixel. Since there is one to one correspondence between the even (zero sum) trixels on the triangular grid and the hexels of the hexagonal grid (main cell with strict 2-neighbors in the triangular grid gets mapped to the main cell with the usual neighbors in the hexagonal grid), the results give us information on the size of the bijective regions after the digitized rotations on the hexagonal grid. First half of the paper considers digitized rotations of the strict 2-neighbors with the given main trixel on the triangular grid, where in the second half the same problem is discussed in a larger scale for all even trixels, and the minimum digital distance from the center of rotation to the first 'error' pixel (in terms of failure of bijectivity) is calculated, and this way the radius of the bijective region on the hexagonal grid is determined. © 2023 IEEE.