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Convert quaternion to Euler angles

Source: R/mocap-angles.R
quaternionToEuler.Rd

Converts a quaternion (w, x, y, z) representation to Euler angles (roll, pitch, yaw) using the specified rotation order.

Usage

quaternionToEuler(w, x, y, z, order = "ZYX", degrees = TRUE)

Arguments

w

Numeric. Scalar (real) part of the quaternion.

x

Numeric. First imaginary component.

y

Numeric. Second imaginary component.

z

Numeric. Third imaginary component.

order

Character. Rotation order. Default "ZYX".

degrees

Logical. If TRUE (default), return Euler angles in degrees. If FALSE, return in radians.

Value

A matrix with columns roll, pitch, yaw. If inputs are scalars, returns a 1-row matrix. If inputs are vectors, returns a matrix with one row per element.

Details

For the "ZYX" (Tait-Bryan) convention:

  • roll = rotation about X axis

  • pitch = rotation about Y axis

  • yaw = rotation about Z axis

The quaternion is assumed to be unit (normalized). If not unit, it is normalized internally before conversion.

References

Winter DA (2009). "Biomechanics and Motor Control of Human Movement." 4th ed. Wiley.

Grood ES, Suntay WJ (1983). "A joint coordinate system for the clinical description of three-dimensional motions: application to the knee." Journal of Biomechanical Engineering, 105(2), 136-144.

See also

eulerToQuaternion(), calculateJointAngles(), vectorAngle()

Examples

# Identity quaternion -> zero Euler angles
quaternionToEuler(1, 0, 0, 0)
#>      roll pitch yaw
#> [1,]    0     0   0

# 90-degree rotation about Z axis
quaternionToEuler(cos(pi/4), 0, 0, sin(pi/4))
#>      roll pitch yaw
#> [1,]    0     0  90