It is important to note that the meanings attached to an NDF's axis arrays are defined rather precisely. In particular, note that the axis centre array specifies the position of the geometrical centre of a pixel, i.e. the mid-point between its edges, so that a pixel will always extend by an equal amount on either side of this position.
The edges of adjacent pixels will therefore only meet exactly (i.e. there will be no overlap or gap) if their centre and width values are related in the correct way. To be precise, adjacent pixels with indices i and i+1 must have centre positions separated by half the sum of their widths if they are to be contiguous along a particular axis, so that:
With contiguous pixels (the normal case), this means that the axis
centre and width arrays are not independent.
In fact, either could be derived from the other to within a constant,
but since this constant cannot be found without additional information,
it is often necessary to store both arrays.
However, an important exception occurs if the pixel centres are
evenly spaced, because a convenient method then exists of deriving the
width array from the centre array so that contiguous
pixels
always result.
This is the method used to generate default axis width values when
necessary (§).
To avoid any potential ambiguity about the interpretation of axis array values and whether an NDF's pixels should be considered contiguous or not, the following recommendations are given about the information which should be stored in axis arrays: