Transform a grid of positions

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).

void astTranGrid( AstMapping
$\ast $this, int ncoord_in,
const int lbnd[], const int ubnd[], double tol, int maxpix, int forward, int ncoord_out, int
outdim, double $\ast $out
);

Pointer to the Mapping to be applied.

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).

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. 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.

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.

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.

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. 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`"`

. 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. 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). If the output grid is so large that
an integer pixel index, (or a count of pixels) could exceed the largest value that can
be represented by a 4-byte integer, then the alternative

`"`

8-byte`"`

interface for this
function should be used. This alternative interface uses 8 byte integer arguments
(instead of 4-byte) to hold pixel indices and pixel counts. Specifically, the
arguments `"`

lbnd`"`

, `"`

ubnd`"`

, `"`

outdim`"`

are changed from type `"`

int`"`

to type `"`

int64_t`"`

(defined in header file stdint.h). The function name is changed by
appending the digit `"`

8`"`

to the name. Thus, astTranGrid becomes astTranGrid8.
Copyright (C) 2021 East Asian Observatory