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rotvec_c

Table of contents
 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

```   rotvec_c ( Transform a vector via a rotation )

void rotvec_c ( ConstSpiceDouble  v1    [3],
SpiceDouble       angle,
SpiceInt          iaxis,
SpiceDouble       vout  [3] )

```

#### Abstract

```   Transform a vector to a new coordinate system rotated by `angle'
radians about axis `iaxis'. This transformation rotates `v1' by
-angle radians about the specified axis.
```

#### Required_Reading

```   None.
```

#### Keywords

```   ROTATION
VECTOR

```

#### Brief_I/O

```   VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
v1         I   Vector whose coordinate system is to be rotated.
angle      I   Angle of rotation in radians.
iaxis      I   Axis of rotation (X=1, Y=2, Z=3).
vout       O   Resulting vector expressed in the new coordinate
system.
```

#### Detailed_Input

```   v1          is a vector (typically representing a vector fixed
in inertial space) which is to be expressed in another
coordinate system. The vector remains fixed but the
coordinate system changes.

angle       is an angle given in radians, through which the rotation
is performed.

iaxis       is the index of the axis of rotation. The X, Y, and Z
axes have indices 1, 2 and 3 respectively.
```

#### Detailed_Output

```   vout        is the vector expressed in the new coordinate system
specified by the angle of rotation and axis. If

m = [angle]
iaxis

represents the rotation matrix described by the `angle'
and `iaxis', (refer to the routine rotate_c) then

vout =  m * v1  = [angle]      * v1
iaxis
```

#### Parameters

```   None.
```

#### Exceptions

```   Error free.

1)  If the `iaxis' index is not in the range 1 to 3, it will be
treated the same as that integer 1, 2, or 3 that is congruent
to it mod 3.
```

#### Files

```   None.
```

#### Particulars

```   A rotation about the first, i.e. X-axis, is described by

.-                              -.
|   1       0            0       |
|   0   cos(theta)   sin(theta)  |
|   0  -sin(theta)   cos(theta)  |
`-                              -'

A rotation about the second, i.e. Y-axis, is described by

.-                              -.
|   cos(theta)   0  -sin(theta)  |
|       0        1       0       |
|   sin(theta)   1   cos(theta)  |
`-                              -'

A rotation about the third, i.e. Z-axis, is described by

.-                              -.
|   cos(theta)   sin(theta)   0  |
|  -sin(theta)   cos(theta)   0  |
|       0            0        1  |
`-                              -'

rotvec_c decides which form is appropriate according to the value
of `iaxis' and applies the rotation to the input vector.
```

#### Examples

```   The numerical results shown for this example 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) Apply a rotation of -45.0 degrees about the +Z axis to
a 3 dimensional vector.

Example code begins here.

/.
Program rotvec_ex1
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables.
./
SpiceDouble          angle;
SpiceDouble          vout   [3];

SpiceInt             iaxis;

/.
Input values.
./
SpiceDouble          v1     [3] = { 1.414, 0.0, 0.0 };

angle = pi_c ( )/4;
iaxis = 3;

/.
Rotate `v1' by `angle' radians about `iaxis'.
./
rotvec_c ( v1, angle, iaxis, vout );

printf( "Input vector  : %9.3f %9.3f %9.3f\n",
v1[0], v1[1], v1[2] );
printf( "Rotated vector: %9.3f %9.3f %9.3f\n",
vout[0], vout[1], vout[2] );

return ( 0 );
}

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

Input vector  :     1.414     0.000     0.000
Rotated vector:     1.000    -1.000     0.000
```

#### Restrictions

```   None.
```

#### Literature_References

```   None.
```

#### Author_and_Institution

```   N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)
E.D. Wright         (JPL)
```

#### Version

```   -CSPICE Version 1.1.2, 04-AUG-2021 (JDR)

Edited the header to comply with NAIF standard.

Created complete code example from existing code fragments.

-CSPICE Version 1.1.1, 04-OCT-1999 (NJB)

Procedure line and abstract and were changed to dispel the
impression that the input vector is rotated by +angle
radians about the specified axis.

-CSPICE Version 1.1.0, 22-OCT-1998 (NJB)

Made input vector const.

-CSPICE Version 1.0.0, 08-FEB-1998 (EDW)
```

#### Index_Entries

```   rotate a vector
```
`Fri Dec 31 18:41:11 2021`