The distance \(d\) between two points \(p\) and \(q\) is then defined as the number of squares in the rectangle formed by the line from \(p\) to \(q\) and the width \(N_{D}\), divided by \(N_{D}\). The idea is that, although in a discrete geometry lines must necessarily have a width, this is not an essential feature, so it can be divided out.  Hence: