Index Page eul2m_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

       void eul2m_c ( SpiceDouble  angle3,
                      SpiceDouble  angle2,
                      SpiceDouble  angle1,
                      SpiceInt     axis3,
                      SpiceInt     axis2,
                      SpiceInt     axis1,
                      SpiceDouble  r [3][3] )

#### Abstract

       Construct a rotation matrix from a set of Euler angles.

#### Required_Reading

       ROTATION

#### Keywords

       MATRIX
       ROTATION
       TRANSFORMATION

#### Brief_I/O

       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       angle3,
       angle2,
       angle1     I   Rotation angles about third, second, and first
                      rotation axes (radians).
       axis3,
       axis2,
       axis1      I   Axis numbers of third, second, and first rotation
                      axes.

       r          O   Product of the 3 rotations.

#### Detailed_Input

       angle3,
       angle2,
       angle1,

       axis3,
       axis2,
       axis1          are, respectively, a set of three angles and three
                      coordinate axis numbers; each pair angleX and
                      axisX specifies a coordinate transformation
                      consisting of a rotation by angleX radians about
                      the coordinate axis indexed by axisX.  These
                      coordinate transformations are typically
                      symbolized by

                         [ angleX ]     .
                                   axisX

                      See the -Particulars section below for details
                      concerning this notation.

                      Note that these coordinate transformations rotate
                      vectors by

                         -angleX

                      radians about the axis indexed by axisX.

                      The values of axisX may be 1, 2, or 3, indicating
                      the x, y, and z axes respectively.

#### Detailed_Output

       r              is a rotation matrix representing the composition
                      of the rotations defined by the input angle-axis
                      pairs.  Together, the three pairs specify a
                      composite transformation that is the result of
                      performing the rotations about the axes indexed
                      by axis1, axis2, and axis3, in that order.  So,

                         r = [ angle3 ]     [ angle2 ]      [ angle1 ]
                                      axis3          axis2           axis1

                      See the -Particulars section below for details
                      concerning this notation.

                      The resulting matrix r may be thought of as a
                      coordinate transformation; applying it to a vector
                      yields the vector's coordinates in the rotated
                      system.

                      Viewing r as a coordinate transformation matrix,
                      the basis that r transforms vectors to is created
                      by rotating the original coordinate axes first by
                      angle1 radians about the coordinate axis indexed
                      by axis1, next by angle2 radians about the
                      coordinate axis indexed by axis2, and finally by
                      angle3 radians about coordinate axis indexed by
                      axis3.  At the second and third steps of this
                      process, the coordinate axes about which rotations
                      are performed belong to the bases resulting from
                      the previous rotations.

#### Parameters

       None.

#### Exceptions

       1)   If any of axis3, axis2, or axis1 do not have values in

               { 1, 2, 3 },

            the error SPICE(BADAXISNUMBERS) is signalled.

#### Files

       None.

#### Particulars

     section below for details
                      concerning this notation.

                      Note that these coordinate transformations rotate
                      vectors by

                         -angleX

                      radians about the axis indexed by axisX.

                      The values of axisX may be 1, 2, or 3, indicating
                      the x, y, and z axes respectively.

#### Examples

       1)  Create a coordinate transformation matrix by rotating
           the original coordinate axes first by 30 degrees about
           the z axis, next by 60 degrees about the y axis resulting
           from the first rotation, and finally by -50 degrees about
           the z axis resulting from the first two rotations.

                    /.

                    Create the coordinate transformation matrix

                                  o          o          o
                       R  =  [ -50  ]   [  60  ]   [  30  ]
                                     3          2          3

                    All angles in radians, please.   The CSPICE
                    function rpd_c (radians per degree) gives the
                    conversion factor.

                    The z axis is `axis 3'; the y axis is `axis 2'.
                    ./

                    angle1 = rpd_c() *  30.;
                    angle2 = rpd_c() *  60.;
                    angle3 = rpd_c() * -50.;

                    axis1  = 3;
                    axis2  = 2;
                    axis3  = 3;

                    eul2m_c (  angle3, angle2, angle1,
                               axis3,  axis2,  axis1,   r  );

       2)  A trivial example using actual numbers.

           The call

              eul2m_c (  0.,     0.,     halfpi_c(),
                         1,        1,            3,      r  );

           sets r equal to the matrix

              +-                  -+
              |  0      1       0  |
              |                    |
              | -1      0       0  |.
              |                    |
              |  0      0       1  |
              +-                  -+

       3)  Finding the rotation matrix specified by a set of `clock,
           cone, and twist' angles, as defined on the Voyager 2 project:

              Voyager 2 narrow angle camera pointing, relative to the
              Sun-Canopus coordinate system, was frequently specified
              by a set of Euler angles called `clock, cone, and twist'.
              These defined a 3-2-3 coordinate transformation matrix
              TSCTV as the product

                 [ twist ]  [ cone ]   [ clock ] .
                          3         2           3

              Given the angles clock, cone, and twist (in units of
              radians), we can compute tsctv with the call

                 eul2m_c (  twist,  cone,  clock,
                            3,      2,     3,      tsctv  );

       4)  Finding the rotation matrix specified by a set of `right
           ascension, declination, and twist' angles, as defined on the
           Galileo project:

              Galileo scan platform pointing, relative to an inertial
              reference frame, (EME50 variety) is frequently specified
              by a set of Euler angles called `right ascension (RA),
              declination (Dec), and twist'. These define a 3-2-3
              coordinate transformation matrix TISP as the product

                 [ Twist ]  [ pi/2 - Dec ]   [ RA ] .
                          3               2        3

              Given the angles ra, dec, and twist (in units of radians),
              we can compute tisp with the code fragment

                 eul2m_c (  twist,   halfpi_c()-dec,   ra,
                            3,       2,                3,   tisp  );

#### Restrictions

       Beware:  more than one definition of "RA, DEC and twist" exists.

#### Literature_References

       [1]  `Galileo Attitude and Camera Models', JPL IOM 314-323,
             W. M. Owen, Jr.,  Nov. 11, 1983.  NAIF document number
             204.0.

#### Author_and_Institution

       N.J. Bachman   (JPL)

#### Version

       -CSPICE Version 1.0.2, 26-DEC-2006 (NJB)

          Fixed header typo.

       -CSPICE Version 1.0.1, 13-OCT-2004 (NJB)

          Fixed header typo.

       -CSPICE Version 1.0.0 08-FEB-1998 (NJB)

          Based on SPICELIB Version 1.1.1, 10-MAR-1992 (WLT)

#### Index_Entries

       euler angles to matrix

#### Link to routine eul2m_c source file eul2m_c.c

    Wed Apr  5 17:54:35 2017