rotvec

Convert quaternion to rotation vector (radians)

Syntax

rotationVector = rotvec(quat)

Description

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

Convert Quaternion to Rotation Vector in Radians

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

quat — Quaternion to convert

quaternion object | array of quaternion objects

Quaternion to convert, specified as a quaternion object or an array of quaternion objects of any dimensionality.

Output Arguments

rotationVector — Rotation vector (radians)

N-by-3 numeric matrix

Rotation vector representation, in radians, returned as an N-by-3 numeric matrix of rotation vectors, where N is the number of quaternions in the quat argument.

Each row represents the [X Y Z] angles of the rotation vectors. 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

$$q=\cos \left(\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)+\sin \left(\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\left(\text{xi}+y\text{j}+z\text{k}\right),$$

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

Given a quaternion of the form

$$q=a+bi+cj+dk,$$

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

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

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

$$q_{\text{rv}}=\frac{\theta }{\sin \left(\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}[b,c,d].$$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2019b