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eul

Convert transformation or rotation into Euler angles

Since R2023a

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    Syntax

    angles = eul(transformation)
    angles = eul(rotation)
    angles = eul(___,sequence)

    Description

    angles = eul(transformation) converts the rotation of the transformation transformation to the Euler angles angles.

    example

    angles = eul(rotation) converts the rotation rotation to the Euler angles angles.

    example

    angles = eul(___,sequence) specifies the sequence of the Euler-angle rotations sequence using any of the input arguments in previous syntaxes. For example, a sequence of "ZYX" first rotates the z-axis, followed by the y-axis and x-axis.

    Examples

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    Open Live Script

    Create SE(3) transformation with no translation but with a rotation defined by a Euler angles. 

    eul1 = [pi/4 pi/3 pi/8]
    eul1 = 1×3

    0.7854    1.0472    0.3927


    T = se3(eul1,"eul")
    T = se3
    0.3536   -0.4189    0.8364         0
    0.3536    0.8876    0.2952         0
   -0.8660    0.1913    0.4619         0
         0         0         0    1.0000

    Get the Euler angles from the transformation.

    eul2 = eul(T)
    eul2 = 1×3

    0.7854    1.0472    0.3927
    Open Live Script

    Create SO(3) rotation defined by a Euler angles. 

    eul1 = [pi/4 pi/3 pi/8]
    eul1 = 1×3

    0.7854    1.0472    0.3927


    R = so3(eul1,"eul")
    R = so3
    0.3536   -0.4189    0.8364
    0.3536    0.8876    0.2952
   -0.8660    0.1913    0.4619

    Get the Euler angles from the transformation.

    eul2 = eul(R)
    eul2 = 1×3

    0.7854    1.0472    0.3927

    Input Arguments

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    Transformation, specified as an se3 object or as an N-element array of se3 objects. N is the total number of transformations.

    Rotation, specified as an so3 object or as an N-element array of so3 objects. N is the total number of rotations.

    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

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    Euler angles, returned as an M-by-3 matrix of Euler rotation angles. Each row represents one Euler angle set.

    Version History

    Introduced in R2023a

    See Also

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