Each input coordinate value is first scaled to give the index of an entry in the table by subtracting a starting value (the input coordinate corresponding to the first table entry) and dividing by an increment (the difference in input coordinate value between adjacent table entries).
The resulting index will usually contain a fractional part, so the output coordinate value is then generated by interpolating linearly between the appropriate entries in the table. If the index lies outside the range of the table, linear extrapolation is used based on the two nearest entries (i.e. the two entries at the start or end of the table, as appropriate). If either of the entries used for the interplation has a value of AST__BAD, then the interpolated value is returned as AST__BAD.
If the lookup table entries increase or decrease monotonically (ignoring any flat sections), then the inverse transformation may also be performed.
AST A Library for Handling World Coordinate Systems in Astronomy