quat2eul

Convert quaternion to Euler angles

Syntax

eul = quat2eul(quat)

eul = quat2eul(quat,sequence)

[eul,eulAlt] = quat2eul(___)

Description

eul = quat2eul(quat) converts a quaternion rotation, quat, to the corresponding Euler angles, eul. The default order for Euler angle rotations is "ZYX".

eul = quat2eul(quat,sequence) converts a quaternion into Euler angles. The Euler angles are specified in the axis rotation sequence, sequence. The default order for Euler angle rotations is "ZYX".

[eul,eulAlt] = quat2eul(___) also returns an alternate set of Euler angles that represents the same rotation eulAlt.

Examples

Convert Quaternion to Euler Angles

quat = [0.7071 0.7071 0 0];
eulZYX = quat2eul(quat)

eulZYX = 1×3

         0         0    1.5708

Convert Quaternion to Euler Angles Using ZYZ Axis Order

quat = [0.7071 0.7071 0 0];
eulZYZ = quat2eul(quat,'ZYZ')

eulZYZ = 1×3

   -1.5708    1.5708    1.5708

Input Arguments

quat — Unit quaternion

n-by-4 matrix | n-element vector of quaternion objects

Unit quaternion, specified as an n-by-4 matrix or n-element vector of quaternion objects containing n quaternions. If the input is a matrix, each row is a quaternion vector of the form q = [w x y z], with w as the scalar number.

Example: [0.7071 0.7071 0 0]

sequence — Axis-rotation sequence

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

Axis-rotation sequence for the Euler angles, specified as one of these string scalars:

• "ZYX" (default)

• "ZYZ"

• "ZXY"

• "ZXZ"

• "YXY"

• "YZX"

• "YXZ"

• "YZY"

• "XYX"

• "XYZ"

• "XZX"

• "XZY"

Each character indicates the corresponding axis. For example, if the sequence is "ZYX", then the three specified Euler angles are interpreted in order as a rotation around the z-axis, a rotation around the y-axis, and a rotation around the x-axis. When applying this rotation to a point, it will apply the axis rotations in the order x, then y, then z.

Data Types: string | char

Output Arguments

eul — Euler rotation angles

n-by-3 matrix

Euler rotation angles in radians, returned as an n-by-3 array of Euler rotation angles. Each row represents one Euler angle set.

Example: [0 0 1.5708]

eulAlt — Alternate Euler rotation angle solution

n-by-3 matrix

Alternate Euler rotation angle solution in radians, returned as an n-by-3 array of Euler rotation angles. Each row represents one Euler angle set.

Example: [0 0 1.5708]

Extended Capabilities

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

Version History

Introduced in R2015a

R2024b: Additional Euler sequence support

quat2eul supports additional Euler sequences for the sequence argument. These are all the supported Euler sequences:

• "ZYX"

• "ZYZ"

• "ZXY"

• "ZXZ"

• "YXY"

• "YZX"

• "YXZ"

• "YZY"

• "XYX"

• "XYZ"

• "XZX"

• "XZY"

R2020a: Alternate Euler angle output

quat2eul now optionally outputs an alternate set of Euler angles that also represent the same rotation as the original output Euler angles.