In all the following descriptions, the convolving function is designated by , where and are integer pixel numbers. Convolvers must necessarily be of finite extent, hence are only defined over a rectangular array.
It is necessary to have some way to determine the `phase' of any convolver: ie, which pixel of the convolver array should be taken to have row and column indices and equal to zero. The rule applied by asmooth is as follows. If the convolver has for example rows, then row 1 plus the integer part of is taken as the zeroth row. This means that if is odd, the central row is the zeroth row, ie the row indices are taken to extend from to ; if is even, the row indices run from to . The same rule is applied to the columns.