raxisa_c |

Table of contents## Procedureraxisa_c ( Rotation axis of a matrix ) void raxisa_c ( ConstSpiceDouble matrix[3][3], SpiceDouble axis [3], SpiceDouble * angle ) ## AbstractCompute the axis of the rotation given by an input matrix and the angle of the rotation about that axis. ## Required_ReadingROTATION ## KeywordsANGLE MATRIX ROTATION ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- matrix I 3x3 rotation matrix in double precision. axis O Axis of the rotation. angle O Angle through which the rotation is performed. ## Detailed_Inputmatrix is a 3x3 rotation matrix in double precision. ## Detailed_Outputaxis is a unit vector pointing along the axis of the rotation. In other words, `axis' is a unit eigenvector of the input matrix, corresponding to the eigenvalue 1. If the input matrix is the identity matrix, `axis' will be the vector (0, 0, 1). If the input rotation is a rotation by pi radians, both `axis' and -axis may be regarded as the axis of the rotation. angle is the angle between `v' and matrix*v for any non-zero vector `v' orthogonal to `axis'. `angle' is given in radians. The angle returned will be in the range from 0 to pi radians. ## ParametersNone. ## Exceptions1) If the input matrix is not a rotation matrix (where a fairly loose tolerance is used to check this), an error is signaled by a routine in the call tree of this routine. 2) If the input matrix is the identity matrix, this routine returns an angle of 0.0, and an axis of ( 0.0, 0.0, 1.0 ). ## FilesNone. ## ParticularsEvery rotation matrix has an axis `a' such any vector `v' parallel to that axis satisfies the equation v = matrix * v This routine returns a unit vector `axis' parallel to the axis of the input rotation matrix. Moreover for any vector `w' orthogonal to the axis of the rotation, the two vectors axis, w x (matrix*w) (where "x" denotes the cross product operation) will be positive scalar multiples of one another (at least to within the ability to make such computations with double precision arithmetic, and under the assumption that `matrix' does not represent a rotation by zero or pi radians). The angle returned will be the angle between `w' and matrix*w for any vector orthogonal to `axis'. If the input matrix is a rotation by 0 or pi radians some choice must be made for the axis returned. In the case of a rotation by 0 radians, `axis' is along the positive z-axis. In the case of a rotation by 180 degrees, two choices are possible. The choice made this routine is unspecified. ## ExamplesThe 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) Given an axis and an angle of rotation about that axis, determine the rotation matrix. Using this matrix as input, compute the axis and angle of rotation, and verify that the later are equivalent by subtracting the original matrix and the one resulting from using the computed axis and angle of rotation on the axisar_c call. Example code begins here. /. Program raxisa_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables ./ SpiceDouble angle; SpiceDouble angout; SpiceDouble axout [3]; SpiceDouble r [3][3]; SpiceDouble rout [3][3]; SpiceInt i; /. Define an axis and an angle for rotation. ./ SpiceDouble axis [3] = { 1.0, 2.0, 3.0 }; angle = 0.1 * twopi_c ( ); /. Determine the rotation matrix. ./ axisar_c ( axis, angle, r ); /. Now calculate the rotation axis and angle based on the matrix as input. ./ ## Restrictions1) If the input matrix is not a rotation matrix but is close enough to pass the tests this routine performs on it, no error will be signaled, but the results may have poor accuracy. 2) The input matrix is taken to be an object that acts on (rotates) vectors---it is not regarded as a coordinate transformation. To find the axis and angle of a coordinate transformation, input the transpose of that matrix to this routine. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.L. Taber (JPL) F.S. Turner (JPL) ## Version-CSPICE Version 1.0.2, 05-JUL-2021 (JDR) Edited the header to comply with NAIF standard. Added complete code examples. -CSPICE Version 1.0.1, 05-JAN-2005 (NJB) (WLT) (FST) Various header updates were made to reflect changes made to the underlying SPICELIB Fortran code. Miscellaneous header corrections were made as well. -CSPICE Version 1.0.0, 31-MAY-1999 (WLT) (NJB) ## Index_Entriesrotation axis of a matrix |

Fri Dec 31 18:41:11 2021