CL_rot_defRot2Ax

Description

• Computes the rotation, combination of 2 rotations around 2 axes, that transforms a vector (u) into another vector (v).

  The rotation is returned as a quaternion, and the corresponding rotation angles are also returned.

  There are two solutions (in usual situations):

  (qa, angsa): solution such that the second rotation angle is minimal.

  (qb, angsb): solution such that the second rotation angle is maximal.

  axis1 and axis2 can either be vectors (3xN) or axes numbers (1 for x-axis, 2 for y-axis or 3 for z-axis). The axes should be perpendicular to one another. If they are numbers, the vectors u and v must be given in the frame where the axes are basis vectors (coordinates = [1;0;0], [0;1;0], or [0;0;1]).

  Indices for which the rotation doesn't exist or is not uniquely defined are returned in Inok.

• Notes:

  - If no rotation exists, the rotation computed is such that the image of u is as close to v as possible.

  - If the axes are given as vectors, the coordinates are those of the vectors not considering the effect of the rotations.

  - If the axes are colinear, the results are set to %nan.

Parameters

u:

Vector to be rotated (3xN or 3x1)

v:

Desired image of u by the rotation (3xN or 3x1)

axis1:

Axis vector (3xN or 3x1) or axis number (1x1) for the first rotation

axis2:

Axis vector (3xN or 3x1) or axis number (1x1) for the second rotation

numsol:

(optional, integer) Number of solutions returned: 1 or 2. Default is 1

qa:

Quaternion for the 1st solution (dim N)

angsa:

Rotation angles for the 1st solution (2xN)

qb:

Quaternion for the 2nd solution (dim N)

angsb:

Rotation angles for the 2nd solution (2xN)

Inok:

Indices for which the rotation is not uniquely defined, or the desired target vector cannot be reached

Authors

• CNES - DCT/SB

See also

• CL_rot_defQuat

• CL_rot_defRotVec

• CL_rot_defRot1Ax

Examples

// Example1: X axis then Y u = [ 1 ; 2 ; 3 ]; v = [ 3 ; 1 ; 2 ]; n1 = 1; n2 = 2; [qa, angsa, Inok] = CL_rot_defRot2Ax(u, v, n1, n2); // Check results : v2 = CL_rot_rotVect(qa,u) // == v // Example2: axes = vectors u = [ 1 ; 2 ; 3 ]; v = [ 3 ; 1 ; 2 ]; axis1 = [-2;3;4]; axis2 = [1;0;1]; [qa, angsa, qb, angsb, Inok] = CL_rot_defRot2Ax(u, v, axis1, axis2, numsol=2); // Check results : v2a = CL_rot_rotVect(qa,u) // == v v2b = CL_rot_rotVect(qb,u) // == v