# eul2quat

Convert Euler angles to quaternion

## Description

quat = eul2quat(eul) converts a given set of Euler angles, eul, to the corresponding quaternion, quat. The default order for Euler angle rotations is "ZYX".

example

quat = eul2quat(eul,sequence) converts a set of Euler angles into a quaternion. The Euler angles are specified in the axis rotation sequence, sequence. The default order for Euler angle rotations is "ZYX".

example

## Examples

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eul = [0 pi/2 0];
qZYX = eul2quat(eul)
qZYX = 1×4

0.7071         0    0.7071         0

eul = [pi/2 0 0];
qZYZ = eul2quat(eul,"ZYZ")
qZYZ = 1×4

0.7071         0         0    0.7071

## Input Arguments

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Euler rotation angles in radians, specified as an n-by-3 array of intrinsic Euler rotation angles. Each row represents one Euler angle set in the sequence defined by the sequence argument. For example, with the default sequence "ZYX", each row of eul is of the form [zAngle yAngle xAngle].

Example: [0 0 1.5708]

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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Unit quaternion, returned as an n-by-4 matrix containing n quaternions. Each quaternion, one per row, is of the form q = [w x y z], with w as the scalar number.

Example: [0.7071 0.7071 0 0]

## Version History

Introduced in R2015a

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