Axis Extrapolation  

When using NDF sections, the possibility also exists of reading axis array values from sections which refer to super-sets of the associated base NDF (§). Although the section's axis arrays may be in a defined state (values having previously been assigned via the base NDF), parts of them will still lie outside the bounds of the base NDF, and so cannot have any values. In such cases, axis arrays must be extrapolated in order to return useful values. This process uses a set of axis extrapolation rules which are an extension of the rules normally used to generate the default axis values (§), as follows:

Centre:

Axis centre arrays are linearly extrapolated from the centre values of the two nearest base-NDF pixels on the same axis. If only one of these pixels exists, then the extrapolation assumes unit spacing between pixel centres.

Width:

If an axis width array is in a defined state, it is extrapolated by duplicating the nearest base-NDF width value on the same axis. If it is in an undefined state, its new values are derived from the corresponding extrapolated centre values by employing the usual method for generating default axis width values (§)--this normally gives rise to width values which match the pixel centre spacing of the two nearest base-NDF pixels on the same axis.

Variance:

Axis variance arrays are always extrapolated by padding with the value zero.

There is also the possibility that an NDF section may have more dimensions than its associated base NDF (see §), in which case associated axis components will also exist. These ``virtual'' axis components may be accessed in the same way as those associated with other dimensions, but they are always regarded as being in an undefined state. Default values will be supplied for them, if necessary, using the normal defaulting rules (see §), but any new values assigned will simply be discarded.