Digitized Rotations of Closest Neighborhood on the Triangular Grid

Abstract

Rigid motions on the plane play an important role in image processing and in image manipulation. They have many properties including the bijectivity and the isometry. On the other hand, digitized rigid motions may fail to satisfy this injectivity or surjectivity properties. Pluta et al. investigated digitized rigid motions locally on the square grid and the hexagonal grid by using neighborhood motion maps. In this paper we show digitized rigid rotations of a pixel and its closest neighbors on the triangular grid. In particular, different rotation centers are considered with respect to the corresponding main pixel, e.g. edge midpoints and corner points. Angles of all bijective and non-bijective rotations are proven for rotations described above.