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sphrec_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

```   sphrec_c ( Spherical to rectangular coordinates )

void sphrec_c ( SpiceDouble    r,
SpiceDouble    colat,
SpiceDouble    slon,
SpiceDouble    rectan[3] )

```

#### Abstract

```   Convert from spherical coordinates to rectangular coordinates.
```

```   None.
```

#### Keywords

```   CONVERSION
COORDINATES

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
r          I   Distance of a point from the origin.
colat      I   Angle of the point from the Z-axis in radians.
slon       I   Angle of the point from the XZ plane in radians.
rectan     O   Rectangular coordinates of the point.
```

#### Detailed_Input

```   r           is the distance of the point from the origin.

colat       is the angle between the point and the positive z-axis in

slon        is the angle of the projection of the point to the XY plane
from the positive X-axis in radians. The positive Y-axis is
```

#### Detailed_Output

```   rectan      are the rectangular coordinates of a point.
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.
```

#### Files

```   None.
```

#### Particulars

```   This routine returns the rectangular coordinates of a point
whose position is input in spherical coordinates.

Spherical coordinates are defined by a distance from a central
reference point, an angle from a reference meridian, and an angle
from the z-axis. The co-latitude of the positive Z-axis is
zero. The longitude of the posive Y-axis is PI/2 radians.
```

#### 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) Compute the spherical coordinates of the position of the Moon
as seen from the Earth, and convert them to rectangular
coordinates.

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

KPL/MK

File name: sphrec_ex1.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
---------                     --------
de421.bsp                     Planetary ephemeris
naif0012.tls                  Leapseconds

\begindata

'naif0012.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program sphrec_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

SpiceDouble          colat;
SpiceDouble          et;
SpiceDouble          lt;
SpiceDouble          pos    [3];
SpiceDouble          rectan [3];
SpiceDouble          slon;

/.
Load SPK and LSK kernels, use a meta kernel for
convenience.
./
furnsh_c ( "sphrec_ex1.tm" );

/.
Look up the geometric state of the Moon as seen from
the Earth at 2017 Mar 20, relative to the J2000
reference frame.
./
str2et_c ( "2017 Mar 20", &et );

spkpos_c ( "Moon", et, "J2000", "NONE", "Earth", pos, &lt );

/.
Convert the position vector `pos' to spherical
coordinates.
./
recsph_c ( pos, &radius, &colat, &slon );

/.
Convert the spherical coordinates to rectangular.
./
sphrec_c ( radius, colat, slon, rectan );

printf( " \n" );
printf( "Original rectangular coordinates:\n" );
printf( " \n" );
printf( " X           (km):  %19.8f\n", pos[0] );
printf( " Y           (km):  %19.8f\n", pos[1] );
printf( " Z           (km):  %19.8f\n", pos[2] );
printf( " \n" );
printf( "Spherical coordinates:\n" );
printf( " \n" );
printf( " Colatitude (deg):  %19.8f\n", colat*dpr_c ( ) );
printf( " Longitude  (deg):  %19.8f\n", slon*dpr_c ( ) );
printf( " \n" );
printf( "Rectangular coordinates from sphrec_c:\n" );
printf( " \n" );
printf( " X           (km):  %19.8f\n", rectan[0] );
printf( " Y           (km):  %19.8f\n", rectan[1] );
printf( " Z           (km):  %19.8f\n", rectan[2] );
printf( " \n" );

return ( 0 );
}

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

Original rectangular coordinates:

X           (km):      -55658.44323296
Y           (km):     -379226.32931475
Z           (km):     -126505.93063865

Spherical coordinates:

Colatitude (deg):         108.26566077
Longitude  (deg):         -98.34959789

Rectangular coordinates from sphrec_c:

X           (km):      -55658.44323296
Y           (km):     -379226.32931475
Z           (km):     -126505.93063865

2) Create a table showing a variety of spherical coordinates
and the corresponding rectangular coordinates.

Corresponding spherical and rectangular coordinates are
listed to three decimal places. Input angles are in degrees.

Example code begins here.

/.
Program sphrec_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

/.
Local variables.
./
SpiceDouble          rcolat;
SpiceDouble          rslon;
SpiceDouble          rectan [3];

SpiceInt             i;

/.
Define the input spherical coordinates. Angles in degrees.
./
SpiceDouble          radius [NREC] = {  0.0,  1.0,     1.0,
1.0,  1.0,     1.0,
1.0,  1.4142,  1.4142,
1.4142,  1.7320          };

SpiceDouble          colat  [NREC] = {  0.0,  90.0,  90.0,
0.0,  90.0,  90.0,
180.0,  90.0,  45.0,
45.0,  54.7356     };

SpiceDouble          slon   [NREC] = {  0.0,   0.0,  90.0,
0.0, 180.0, -90.0,
0.0,  45.0,   0.0,
90.0,  45.0        };

/.
Print the banner.
./
printf( "  radius   colat     slon   rect[0]  rect[1]  rect[2]\n" );
printf( " -------  -------  -------  -------  -------  -------\n" );

/.
Do the conversion.
./
for ( i = 0; i < NREC; i++ )
{

rcolat = colat[i] * rpd_c ( );
rslon  = slon[i]  * rpd_c ( );

sphrec_c ( radius[i], rcolat, rslon, rectan );

printf( "%8.3f %8.3f %8.3f ",  radius[i], colat[i],  slon[i]   );
printf( "%8.3f %8.3f %8.3f\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:

radius   colat     slon   rect[0]  rect[1]  rect[2]
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000    0.000
1.000   90.000    0.000    1.000    0.000    0.000
1.000   90.000   90.000    0.000    1.000    0.000
1.000    0.000    0.000    0.000    0.000    1.000
1.000   90.000  180.000   -1.000    0.000    0.000
1.000   90.000  -90.000    0.000   -1.000    0.000
1.000  180.000    0.000    0.000    0.000   -1.000
1.414   90.000   45.000    1.000    1.000    0.000
1.414   45.000    0.000    1.000    0.000    1.000
1.414   45.000   90.000    0.000    1.000    1.000
1.732   54.736   45.000    1.000    1.000    1.000
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   J. Diaz del Rio     (ODC Space)
B.V. Semenov        (JPL)
W.L. Taber          (JPL)
E.D. Wright         (JPL)
```

#### Version

```   -CSPICE Version 1.1.0, 05-JUL-2021 (JDR)

Changed the output argument name "lon" to "slon" for
consistency with other routines.

Edited the header to comply with NAIF standard.
```   spherical to rectangular coordinates
`Fri Dec 31 18:41:12 2021`