tform2eul

Extract Euler angles from homogeneous transformation

Syntax

eul = tform2eul(tform)

eul = tform2eul(tform, sequence)

[eul,eulAlt] = tform2eul(___)

Description

eul = tform2eul(tform) extracts the rotational component from a homogeneous transformation, tform, and returns it as Euler angles, eul. The translational components of tform are ignored. The input homogeneous transformation must be in the premultiply form for transformations. The default order for Euler angle rotations is "ZYX".

eul = tform2eul(tform, sequence) extracts the Euler angles, eul, from a homogeneous transformation, tform, using the specified rotation sequence, sequence. The default order for Euler angle rotations is "ZYX".

[eul,eulAlt] = tform2eul(___) also returns an alternate set of Euler angles that represents the same rotation eulAlt.

Examples

Extract Euler Angles from Homogeneous Transformation Matrix

tform = [1 0 0 0.5; 0 -1 0 5; 0 0 -1 -1.2; 0 0 0 1];
eulZYX = tform2eul(tform)

eulZYX = 1×3

         0         0    3.1416

Extract Euler Angles from Homogeneous Transformation Matrix Using ZYZ Rotation

tform = [1 0 0 0.5; 0 -1 0 5; 0 0 -1 -1.2; 0 0 0 1];
eulZYZ = tform2eul(tform,'ZYZ')

eulZYZ = 1×3

         0   -3.1416    3.1416

Input Arguments

tform — Homogeneous transformation

4-by-4-by-n matrix

Homogeneous transformation, specified by a 4-by-4-by-n matrix of n homogeneous transformations. The input homogeneous transformation must be in the premultiply form for transformations.

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

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

tform2eul 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

tform2eul 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.