Table of contents
CSPICE_ROTATE calculates the 3x3 rotation matrix generated
by a rotation of a specified angle about a specified axis.
This rotation operates as a rotation of the coordinate
system.
Given:
angle the angle(s), given in radians, through which the rotation is
performed.
[1,n] = size(angle); double = class(angle)
iaxis the index of the axis of rotation.
[1,1] = size(iaxis); int32 = class(iaxis)
The X, Y, and Z axes have indices 1, 2 and 3 respectively.
the call:
[mout] = cspice_rotate( angle, iaxis )
returns:
mout the rotation matri(x|ces) which describes the rotation of a
reference frame through `angle' radians about the axis whose
index is `iaxis'.
If [1,1] = size(angle) then [3,3] = size(mout)
If [1,n] = size(angle) then [3,3,n] = size(mout)
double = class(mout)
`mout' returns with the same vectorization measure, N,
as `angle'.
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Compute the 3x3 matrix that rotates vectors from one
frame to another frame rotated by pi/10 radians about
+Y with respect to the first frame, and use it to transform
an arbitrary vector from the first frame to the second frame.
Example code begins here.
function rotate_ex1()
%
% Let's pick an arbitrary vector.
%
vec1 = [ 0.2; 0.04; 1.0 ];
fprintf( 'Vector in base frame:\n' )
fprintf( ' %16.12f %16.12f %16.12f\n', vec1 );
%
% Compute Pi/10 frame rotation about the Y axis.
%
rotmat = cspice_rotate( 0.1*cspice_pi, 2 );
%
% Apply the coordinate rotation to the vector.
%
vec2 = rotmat * vec1;
fprintf( 'Vector in rotated frame:\n' )
fprintf( ' %16.12f %16.12f %16.12f\n', vec2 );
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Vector in base frame:
0.200000000000 0.040000000000 1.000000000000
Vector in rotated frame:
-0.118805691116 0.040000000000 1.012859915170
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) 0 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 |
cspice_rotate decides which form is appropriate according to the value
of `iaxis'.
1) If the axis 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.
2) If any of the input arguments, `angle' or `iaxis', is
undefined, an error is signaled by the Matlab error handling
system.
3) If any of the input arguments, `angle' or `iaxis', is not of
the expected type, or it does not have the expected dimensions
and size, an error is signaled by the Mice interface.
None.
None.
MICE.REQ
ROTATION.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Mice Version 1.1.0, 24-AUG-2021 (EDW) (JDR)
Edited the header to comply with NAIF standard. Added
example's problem statement and modified example code accordingly.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.1, 10-MAR-2015 (EDW)
Edited -I/O section to conform to NAIF standard for Mice documentation.
-Mice Version 1.0.0, 10-JAN-2006 (EDW)
generate a rotation matrix
|