quat2angle

Convert quaternion to rotation angles

Syntax

[rotationAng1 rotationAng2 rotationAng3] = quat2angle(q)

[rotationAng1 rotationAng2 rotationAng3] = quat2angle(q,s)

Description

[rotationAng1 rotationAng2 rotationAng3] = quat2angle(q) calculates the set of rotation angles, rotationAng1, rotationAng2, rotationAng3, for a given quaternion, q. The quaternion represents a passive transformation from frame A to frame B. The resulting rotation angles represent a series of right-hand intrinsic passive rotations from frame A to frame B.

[rotationAng1 rotationAng2 rotationAng3] = quat2angle(q,s) calculates the set of rotation angles rotationAng1, rotationAng2, rotationAng3 for a given quaternion, q, and a specified rotation sequence, s.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention. This function normalizes all quaternion inputs.

Examples

Determine Rotation Angles from Quaternion

Determine the rotation angles from q = [1 0 1 0].

[yaw, pitch, roll] = quat2angle([1 0 1 0])

yaw =
     0

pitch =
    1.5708

roll =
     0

Determine Rotation Angles from Multiple Quaternions and Rotation Order

Determine the rotation angles from multiple quaternions.

q = [1 0 1 0; 1 0.5 0.3 0.1];
 [pitch, roll, yaw] = quat2angle(q, 'YXZ')

pitch =
    1.5708
    0.8073
roll =
         0
    0.7702
yaw =
         0
    0.5422

Input Arguments

q — Quaternion

m-by-4 matrix | each element of q must be real number

Quaternion, specified as an m-by-4 matrix containing m quaternions. q has its scalar number as the first column.

Data Types: double

s — Rotation order

ZYX (default) | ZYZ | ZXY | ZXZ | YXZ | YXY | YZX | YZY | XYZ | XYX | XZY | XZX

Rotation order for three rotation angles, where Z is in the z-axis, Y is in the y-axis, and X is in the x-axis.

Data Types: char | string

Output Arguments

rotationAng1 — First rotation angles

m-array

First rotation angles, returned as an m-array, in radians.

rotationAng2 — Second rotation angles

m-array

Second rotation angles, returned as an m-array, in radians.

rotationAng3 — Third rotation angles

m-array

Third rotation angles, returned as an m-array, in radians.

Limitations

• The 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' implementations generate a rotationAng2 angle that lies between ±90 degrees, and rotationAng1 and rotationAng3 angles that lie between ±180 degrees.

• The 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' implementations generate a rotationAng2 angle that lies between 0 and 180 degrees, and rotationAng1 and rotationAng3 angles that lie between ±180 degrees.

Version History

Introduced in R2007b