rotm2eul

Convert rotation matrix to Euler angles

Syntax

eul = rotm2eul(rotm)

eul = rotm2eul(rotm,sequence)

[eul,eulAlt] = rotm2eul(___)

Description

eul = rotm2eul(rotm) converts a rotation matrix, rotm, to the corresponding Euler angles, eul. The input rotation matrix must be in the premultiply form for rotations. The default order for Euler angle rotations is "ZYX".

eul = rotm2eul(rotm,sequence) converts a rotation matrix to Euler angles. The Euler angles are specified in the axis rotation sequence, sequence. The default order for Euler angle rotations is "ZYX".

[eul,eulAlt] = rotm2eul(___) also returns an alternate set of Euler angles that represents the same rotation eulAlt.

Examples

Convert Rotation Matrix to Euler Angles

rotm = [0 0 1; 0 1 0; -1 0 0];
eulZYX = rotm2eul(rotm)

eulZYX = 1×3

         0    1.5708         0

Convert Rotation Matrix to Euler Angles Using ZYZ Axis Order

rotm = [0 0 1; 0 1 0; -1 0 0];
eulZYZ = rotm2eul(rotm,'ZYZ')

eulZYZ = 1×3

   -3.1416   -1.5708   -3.1416

Input Arguments

rotm — Rotation matrix

3-by-3-by-n matrix

Rotation matrix, specified as a 3-by-3-by-n matrix containing n rotation matrices. Each rotation matrix has a size of 3-by-3 and is orthonormal. The input rotation matrix must be in the premultiply form for rotations.

Note

Rotation matrices that are slightly non-orthonormal can give complex outputs. Consider validating your matrix before inputting to the function.

Example: [0 0 1; 0 1 0; -1 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

R2023a: Additional Euler sequence support

rotm2eul 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

rotm2eul now optionally outputs an alternate set of Euler angles eulAlt that also represent the same rotation as the original output Euler angles eul. So if you use eul or eulAlt to rotate a point, the resulting point is the same.