Note that "lbnd" and "ubnd" together define the shape and size of the input grid, its extent along a particular (j'th) dimension being ubnd[j]-lbnd[j]1 (assuming the index "j" to be zero-based). They also define the input grid's coordinate system, each pixel having unit extent along each dimension with integral coordinate values at its centre.
If piece-wise linear approximation is not required, a value of zero may be given. This will ensure that the Mapping is used without any approximation, but may increase execution time.
If the value is too high, discontinuities between the linear approximations used in adjacent panel will be higher. If this is a problem, reduce the tolerance value used.
If a smaller value is used, the input region will first be divided into sub-regions whose size does not exceed "maxpix" grid points in any dimension. Only at this point will attempts at approximation commence.
This value may occasionally be useful in preventing false convergence of the adaptive algorithm in cases where the Mapping appears approximately linear on large scales, but has irregularities (e.g. holes) on smaller scales. A value of, say, 50 to 100 grid points can also be employed as a safeguard in general-purpose software, since the effect on performance is minimal.
If too small a value is given, it will have the effect of inhibiting linear approximation altogether (equivalent to setting "tol" to zero). Although this may degrade performance, accurate results will still be obtained.
AST A Library for Handling World Coordinate Systems in Astronomy