Rotations on the triangular grid: angles of changes of the neighborhood motion map

Abstract

Digital image processing is a well-known field that applies various mathematical methods. Among other parts of image processing the study of digital rotations is an important field that is applied in our everyday life. Digital images are understood in a discrete domain, usually on a periodic grid. On the triangular grid, the digitized rotations of a main triangle pixel (trixel) together with its side neighbors are considered. Given a main triangle pixel lying anywhere on the plane, and the centre of rotation taken to be the midpoint of any triangle pixel, we calculate the rotation angles where the neighborhood motion map (NMM) changes. This occurs when the respective locations of the side neighbor trixels change. An algorithm to compute angles for the following neighborhood motion map changes is also given.