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azlrec_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

```   azlrec_c ( AZ/EL to rectangular coordinates )

void azlrec_c ( SpiceDouble         range,
SpiceDouble         az,
SpiceDouble         el,
SpiceBoolean        azccw,
SpiceBoolean        elplsz,
SpiceDouble         rectan [3] )

```

#### Abstract

```   Convert from range, azimuth and elevation of a point to
rectangular coordinates.
```

```   None.
```

#### Keywords

```   CONVERSION
COORDINATES

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
range      I   Distance of the point from the origin.
azccw      I   Flag indicating how azimuth is measured.
elplsz     I   Flag indicating how elevation is measured.
rectan     O   Rectangular coordinates of a point.
```

#### Detailed_Input

```   range       is the distance of the point from the origin. The
input should be in terms of the same units in which
the output is desired.

Although negative values for `range' are allowed, its
use may lead to undesired results. See the -Exceptions
section for a discussion on this topic.

az          is the azimuth of the point. This is the angle between
the projection onto the XY plane of the vector from
the origin to the point and the +X axis of the
reference frame. `az' is zero at the +X axis.

The way azimuth is measured depends on the value of
the logical flag `azccw'. See the descriptions of the
argument `azccw' for details.

The range (i.e., the set of allowed values) of `az' is
unrestricted. See the -Exceptions section for a
discussion on the `az' range.

el          is the elevation of the point. This is the angle
between the vector from the origin to the point and
the XY plane. `el' is zero at the XY plane.

The way elevation is measured depends on the value of
the logical flag `elplsz'. See the descriptions of the
argument `elplsz' for details.

The range (i.e., the set of allowed values) of `el' is
[-pi/2, pi/2], but no error checking is done to ensure
that `el' is within this range. See the -Exceptions
section for a discussion on the `el' range.

azccw       is a flag indicating how the azimuth is measured.

If `azccw' is SPICETRUE, the azimuth increases in the
counterclockwise direction; otherwise it increases
in the clockwise direction.

elplsz      is a flag indicating how the elevation is measured.

If `elplsz' is SPICETRUE, the elevation increases from
the XY plane toward +Z; otherwise toward -Z.
```

#### Detailed_Output

```   rectan      is an array containing the rectangular coordinates of
the point.

The units associated with the point are those
associated with the input `range'.
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.

1)  If the value of the input argument `range' is negative
the output rectangular coordinates will be negated, i.e.
the resulting array will be of the same length
but opposite direction to the one that would be obtained
with a positive input argument `range' of value ||RANGE||.

2)  If the value of the input argument `el' is outside the
range [-pi/2, pi/2], the results may not be as
expected.

3)  If the value of the input argument `az' is outside the
range [0, 2*pi], the value will be mapped to a value
inside the range that differs from the input value by an
integer multiple of 2*pi.
```

#### Files

```   None.
```

#### Particulars

```   This routine converts the azimuth, elevation, and range
of a point into the associated rectangular coordinates.

The input is defined by the distance from the center of
the reference frame (range), the angle from a reference
vector (azimuth), and the angle above the XY plane of the
reference frame (elevation).

The way azimuth and elevation are measured depends on the
values given by the user to the `azccw' and `elplsz' logical
flags. See the descriptions of these input arguments
for details.
```

#### Examples

```   The numerical results shown for these examples may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.

1) Create four tables showing a variety of azimuth/elevation
coordinates and the corresponding rectangular coordinates,
resulting from the different choices of the `azccw' and `elplsz'
flags.

Corresponding azimuth/elevation and rectangular coordinates
are listed to three decimal places. Input angles are in
degrees.

Example code begins here.

/.
Program azlrec_ex1
./
#include <stdio.h>
#include <string.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

/.
Local variables.
./
SpiceChar            msg    [31];

SpiceDouble          raz;
SpiceDouble          rel;
SpiceDouble          rectan [3];

SpiceInt             i;
SpiceInt             j;
SpiceInt             n;

/.
Define the input azimuth/elevation coordinates and the
different choices of the `azccw' and `elplsz' flags.
./
SpiceDouble          range  [NREC] = { 0.0,   1.0,   1.0,   1.0,
1.0,   1.0,   1.0,   1.414,
1.414, 1.414, 1.732 };

SpiceDouble          az     [NREC] = {   0.0,   0.0, 270.0,   0.0,
180.0,  90.0,   0.0, 315.0,
0.0, 270.0, 315.0 };

SpiceDouble          el     [NREC] = {   0.0,   0.0,     0.0,
-90.0,   0.0,     0.0,
90.0,   0.0,   -45.0,
-45.0, -35.264,
};

SpiceBoolean         azccw  [2] = { SPICEFALSE,  SPICETRUE };
SpiceBoolean         elplsz [2] = { SPICEFALSE,  SPICETRUE };

/.
Create a table for each combination of `azccw' and `elplsz'.
./
for ( i = 0; i < 2; i++ )
{
for ( j = 0; j < 2; j++ )
{

/.
Display the flag settings.
./
strncpy( msg, "AZCCW = #; ELPLSZ = #", 22 );
repml_c ( msg, "#", azccw[i], 'C', 31, msg );
repml_c ( msg, "#", elplsz[j], 'C', 31, msg );

printf( "\n" );
printf( "%s\n", msg );

/.
Print the banner.
./
printf( "\n" );
printf( "   range      az       el    rect[0]  rect[1]  "
"rect[2]\n" );
printf( "  -------  -------  -------  -------  -------  "
"-------\n" );

/.
Do the conversion. Input angles in degrees.
./
for ( n = 0; n < NREC; n++ )
{
raz = az[n] * rpd_c();
rel = el[n] * rpd_c();

azlrec_c ( range[n], raz,       rel,
azccw[i], elplsz[j], rectan );

printf( "%9.3f %8.3f %8.3f %8.3f %8.3f %8.3f\n",
range[n],  az[n],     el[n],
rectan[0], rectan[1], rectan[2] );
}
}
}

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

AZCCW = False; ELPLSZ = False

range      az       el    rect[0]  rect[1]  rect[2]
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000    0.000    0.000
1.000  270.000    0.000   -0.000    1.000    0.000
1.000    0.000  -90.000    0.000    0.000    1.000
1.000  180.000    0.000   -1.000   -0.000    0.000
1.000   90.000    0.000    0.000   -1.000    0.000
1.000    0.000   90.000    0.000    0.000   -1.000
1.414  315.000    0.000    1.000    1.000    0.000
1.414    0.000  -45.000    1.000    0.000    1.000
1.414  270.000  -45.000   -0.000    1.000    1.000
1.732  315.000  -35.264    1.000    1.000    1.000

AZCCW = False; ELPLSZ = True

range      az       el    rect[0]  rect[1]  rect[2]
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000    0.000    0.000
1.000  270.000    0.000   -0.000    1.000    0.000
1.000    0.000  -90.000    0.000    0.000   -1.000
1.000  180.000    0.000   -1.000   -0.000    0.000
1.000   90.000    0.000    0.000   -1.000    0.000
1.000    0.000   90.000    0.000    0.000    1.000
1.414  315.000    0.000    1.000    1.000    0.000
1.414    0.000  -45.000    1.000    0.000   -1.000
1.414  270.000  -45.000   -0.000    1.000   -1.000
1.732  315.000  -35.264    1.000    1.000   -1.000

AZCCW = True; ELPLSZ = False

range      az       el    rect[0]  rect[1]  rect[2]
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000    0.000    0.000
1.000  270.000    0.000   -0.000   -1.000    0.000
1.000    0.000  -90.000    0.000    0.000    1.000
1.000  180.000    0.000   -1.000    0.000    0.000
1.000   90.000    0.000    0.000    1.000    0.000
1.000    0.000   90.000    0.000    0.000   -1.000
1.414  315.000    0.000    1.000   -1.000    0.000
1.414    0.000  -45.000    1.000    0.000    1.000
1.414  270.000  -45.000   -0.000   -1.000    1.000
1.732  315.000  -35.264    1.000   -1.000    1.000

AZCCW = True; ELPLSZ = True

range      az       el    rect[0]  rect[1]  rect[2]
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000    0.000    0.000    1.000    0.000    0.000
1.000  270.000    0.000   -0.000   -1.000    0.000
1.000    0.000  -90.000    0.000    0.000   -1.000
1.000  180.000    0.000   -1.000    0.000    0.000
1.000   90.000    0.000    0.000    1.000    0.000
1.000    0.000   90.000    0.000    0.000    1.000
1.414  315.000    0.000    1.000   -1.000    0.000
1.414    0.000  -45.000    1.000    0.000   -1.000
1.414  270.000  -45.000   -0.000   -1.000   -1.000
1.732  315.000  -35.264    1.000   -1.000   -1.000

2) Compute the right ascension and declination of the pointing
direction of DSS-14 station at a given epoch.

================

In this example, we will obtain the right ascension and
declination of the pointing direction of the DSS-14 station at
a given epoch, by converting the station's pointing direction
given in azimuth and elevation to rectangular coordinates
in the station topocentric reference frame and applying a
frame transformation from DSS-14_TOPO to J2000, in order to
finally obtain the corresponding right ascension and
declination of the pointing vector.

In order to introduce the usage of the logical flags `azccw'
and `elplsz', we will assume that the azimuth is measured
counterclockwise and the elevation negative towards +Z
axis of the DSS-14_TOPO reference frame.

Kernels
=======

Use the meta-kernel shown below to load the required SPICE
kernels.

KPL/MK

File name: azlrec_ex2.tm

This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.

In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.

The names and contents of the kernels referenced
by this meta-kernel are as follows:

File name                        Contents
---------                        --------
naif0011.tls                     Leapseconds
earth_720101_070426.bpc          Earth historical
binary PCK
earth_topo_050714.tf             DSN station FK

\begindata

'earth_720101_070426.bpc',
'earth_topo_050714.tf'     )

\begintext

End of meta-kernel.

Example code begins here.

/.
Program azlrec_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters
./
#define META         "azlrec_ex2.tm"

/.
Local variables
./
SpiceChar            msg    [41];
SpiceChar          * obstim;
SpiceChar          * ref;

SpiceDouble          az;
SpiceDouble          azr;
SpiceDouble          dec;
SpiceDouble          el;
SpiceDouble          elr;
SpiceDouble          et;
SpiceDouble          jpos   [3];
SpiceDouble          ptarg  [3];
SpiceDouble          r;
SpiceDouble          ra;
SpiceDouble          range;
SpiceDouble          rotate [3][3];

SpiceBoolean         azccw;
SpiceBoolean         elplsz;

/.
./
furnsh_c ( META );

/.
Convert the observation time to seconds past J2000 TDB.
./
obstim = "2003 OCT 13 06:00:00.000000 UTC";

str2et_c ( obstim, &et );

/.
Set the local topocentric frame
./
ref    = "DSS-14_TOPO";

/.
Set the station's pointing direction in azimuth and
elevation. Set arbitrarily the range to 1.0. Azimuth
and elevation shall be given in radians. Azimuth
increases counterclockwise and elevation is negative
towards +Z (above the local horizon)
./
az     =   75.00;
el     =  -27.25;
azr    =   az * rpd_c();
elr    =   el * rpd_c();
r      =    1.00;
azccw  = SPICETRUE;
elplsz = SPICEFALSE;

/.
Obtain the rectangular coordinates of the station's
pointing direction.
./
azlrec_c ( r, azr, elr, azccw, elplsz, ptarg );

/.
Transform the station's pointing vector from the
local topocentric frame to J2000.
./
pxform_c ( ref, "J2000", et, rotate );
mxv_c ( rotate, ptarg, jpos );

/.
Compute the right ascension and declination.
Express both angles in degrees.
./
recrad_c ( jpos, &range, &ra, &dec );
ra =   ra * dpr_c();
dec =   dec * dpr_c();

/.
Display the computed pointing vector, the input
data and resulting the angles.
./
printf( "\n" );
printf( "Pointing azimuth    (deg):  %14.8f\n", az );
printf( "Pointing elevation  (deg):  %14.8f\n", el );

repml_c ( "Azimuth counterclockwise?: #", "#", azccw, 'C', 41, msg );
printf( "%s\n", msg );

repml_c ( "Elevation positive +Z?   : #", "#", elplsz, 'C', 41,
msg );
printf( "%s\n", msg );

printf( "Observation epoch        : %s\n", obstim );
printf( "\n" );
printf( "Pointing direction (normalized):  \n" );
printf( "   %14.8f %14.8f %14.8f\n", ptarg[0], ptarg[1], ptarg[2] );
printf( "\n" );
printf( "Pointing right ascension (deg):  %14.8f\n", ra );
printf( "Pointing declination (deg):      %14.8f\n", dec );
printf( "\n" );

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

Pointing azimuth    (deg):     75.00000000
Pointing elevation  (deg):    -27.25000000
Azimuth counterclockwise?: True
Elevation positive +Z?   : False
Observation epoch        : 2003 OCT 13 06:00:00.000000 UTC

Pointing direction (normalized):
0.23009457     0.85872462     0.45787392

Pointing right ascension (deg):    280.06179939
Pointing declination (deg):         26.92826084
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   J. Diaz del Rio     (ODC Space)
```

#### Version

```   -CSPICE Version 1.0.0, 08-FEB-2021 (JDR)
```

#### Index_Entries

```   range, az and el to rectangular coordinates
range, azimuth and elevation to rectangular
convert range, az and el to rectangular coordinates
convert range, azimuth and elevation to rectangular
```
`Fri Dec 31 18:41:01 2021`