CL_rot_defRot1Ax

Description

• Computes the rotation around one axis so that the angle between the image of a vector (u) and a vector d is equal to target_ang.

  That is to say, the rotation R is such that: R(u)=v and angle(v,d)=target_ang. There can be 2 solutions (in usual situations).

  Each rotation is returned as a quaternion, and the corresponding rotation angle is also returned.

  If the condition "angle(v,d)=target_ang" cannot be achieved, the returned rotations are identical and they are computed such that "|angle(v,d)-target_ang|" is minimal. The corresponding indices are returned in Inok.

  When 2 solutions exist:

  qa is the solution with minimal rotation angle.

  qb is the solution with maximal rotation angle.

  The argument axis can either be a vector (3xN) or an axis number (1=x,2=y or 3=z) (1x1). If it is a number, the vectors u and d must be given in the frame where the axis is one of the basis vectors (coordinates = [1;0;0], [0;1;0], or [0;0;1]).

Parameters

u:

Vector to be rotated (3xN or 3x1)

axis:

Axis: vector (3xN or 3x1) or number (1x1)

d:

Some direction (3xN or 3x1)

target_ang:

(optional) Desired angle between d and the image of u by the rotation (1xN or 1x1)

numsol:

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

qa:

Quaternion that defines the rotation (first solution) (dim N)

anga:

Rotation angle (first solution) (1xN)

qb:

Quaternion that defines the rotation (second solution) (dim N)

angb:

Rotation angle (second solution) (1xN)

Inok:

Indices for which the desired angle between d and the image of u by the rotation cannot be achieved.

Authors

• CNES - DCT/SB

See also

• CL_rot_defQuat

• CL_rot_defRotVec

• CL_rot_defRot2Ax

Examples

// Example1: Rotation about x-axis that transforms // u into a vector perpendicular to d u = [ 1 ; 2 ; 3 ]; d = [ 3 ; 1 ; 2 ]; [q, ang, Inok] = CL_rot_defRot1Ax(u, 1, d, %pi/2); // Check result : v = CL_rot_rotVect(q,u); CL_vectAngle(v,d) // == %pi/2 // Example2: Rotation about an axis that transforms u // into a vector as close as possible to d u = [ 1 ; 2 ; 3 ]; d = [ 3 ; 1 ; 2 ]; axis = [-2;3;4]; [q, ang, Inok] = CL_rot_defRot1Ax(u, axis, d, 0); // Check result : ang = CL_vectAngle(d,CL_rot_rotVect(q,u)) angmin_approx = min(CL_vectAngle(d,CL_rot_rotVect( .. CL_rot_axAng2quat(axis,linspace(0,2*%pi,200)),u)))