rotvec

Convert quaternion to rotation vector (radians)

Description

example

rotationVector = rotvec(quat) converts the quaternion array, quat, to an N-by-3 matrix of equivalent rotation vectors in radians. The elements of quat are normalized before conversion.

Examples

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Convert a random quaternion scalar to a rotation vector in radians

quat = quaternion(randn(1,4));
rotvec(quat)
ans = 1×3

1.6866   -2.0774    0.7929

Input Arguments

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Quaternion to convert, specified as scalar quaternion, vector, matrix, or multidimensional array of quaternions.

Data Types: quaternion

Output Arguments

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Rotation vector representation, returned as an N-by-3 matrix of rotations vectors, where each row represents the [X Y Z] angles of the rotation vectors in radians. The ith row of rotationVector corresponds to the element quat(i).

The data type of the rotation vector is the same as the underlying data type of quat.

Data Types: single | double

Algorithms

All rotations in 3-D can be represented by a three-element axis of rotation and a rotation angle, for a total of four elements. If the rotation axis is constrained to be unit length, the rotation angle can be distributed over the vector elements to reduce the representation to three elements.

Recall that a quaternion can be represented in axis-angle form

$q=\mathrm{cos}\left(\theta }{2}\right)+\mathrm{sin}\left(\theta }{2}\right)\left(\text{xi}+y\text{j}+z\text{k}\right),$

where θ is the angle of rotation and [x,y,z] represent the axis of rotation.

Given a quaternion of the form

$q=a+bi+cj+dk\text{\hspace{0.17em}},$

you can solve for the rotation angle using the axis-angle form of quaternions:

$\theta =2{\mathrm{cos}}^{-1}\left(a\right).$

Assuming a normalized axis, you can rewrite the quaternion as a rotation vector without loss of information by distributing θ over the parts b, c, and d. The rotation vector representation of q is

${q}_{\text{rv}}=\frac{\theta }{\mathrm{sin}\left(\theta }{2}\right)}\left[b,c,d\right].$