astTranGrid - Transform a grid of positions

**Description:**- This function uses the supplied Mapping to transforms a regular square grid of points covering a specified box. It attempts to do this quickly by first approximating the Mapping with a linear transformation applied over the whole region of the input grid which is being used. If this proves to be insufficiently accurate, the input region is sub-divided into two along its largest dimension and the process is repeated within each of the resulting sub-regions. This process of sub-division continues until a sufficiently good linear approximation is found, or the region to which it is being applied becomes too small (in which case the original Mapping is used directly).

**Synopsis:**`void astTranGrid( AstMapping this, int ncoord_in, const int lbnd[], const int ubnd[], double tol, int maxpix, int forward, int ncoord_out, int outdim, double out );`

**Parameters:****this**- Pointer to the Mapping to be applied.
**ncoord_in**- The number of coordinates being supplied for each box corner (i.e. the number of dimensions of the space in which the input points reside).
**lbnd**-
Pointer to an array of integers, with
`"`ncoord_in`"`elements, containing the coordinates of the centre of the first pixel in the input grid along each dimension. **ubnd**-
Pointer to an array of integers, with
`"`ncoord_in`"`elements, containing the coordinates of the centre of the last pixel in the input grid along each dimension.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. **tol**-
The maximum tolerable geometrical distortion which may be
introduced as a result of approximating non-linear Mappings
by a set of piece-wise linear transformations. This should be
expressed as a displacement within the output coordinate system
of the Mapping.
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.

**maxpix**-
A value which specifies an initial scale size (in input grid points)
for the adaptive algorithm which approximates non-linear Mappings
with piece-wise linear transformations. Normally, this should
be a large value (larger than any dimension of the region of
the input grid being used). In this case, a first attempt to
approximate the Mapping by a linear transformation will be
made over the entire input region.
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. **forward**- A non-zero value indicates that the Mapping's forward coordinate transformation is to be applied, while a zero value indicates that the inverse transformation should be used.
**ncoord_out**-
The number of coordinates being generated by the Mapping for
each output point (i.e. the number of dimensions of the
space in which the output points reside). This need not be
the same as
`"`ncoord_in`"`. **outdim**-
The number of elements along the second dimension of the
`"`out`"`array (which will contain the output coordinates). The value given should not be less than the number of points in the grid. **out**-
The address of the first element in a 2-dimensional array of
shape
`"`[ncoord_out][outdim]`"`, into which the coordinates of the output (transformed) points will be written. These will be stored such that the value of coordinate number`"`coord`"`for output point number`"`point`"`will be found in element`"`out[coord][point]`"`. The points are ordered such that the first axis of the input grid changes most rapidly. For example, if the input grid is 2-dimensional and extends from (2,-1) to (3,1), the output points will be stored in the order (2,-1), (3, -1), (2,0), (3,0), (2,1), (3,1).

**Notes:**

Starlink User Note 211

R.F. Warren-Smith & D.S. Berry

7th December 2012

E-mail:starlink@jiscmail.ac.uk

Copyright (C) 2012 Science \& Technology Facilities Council