# Orientation, Position, and Coordinate Systems

Quaternions, Euler angles, rotation matrices, and conversions

Represent orientation and rotation using the `quaternion` data type. Convert between quaternions and Euler angles, rotation matrices, and rotation vectors using the `euler`, `rotmat`, and `rotvec` functions.

To learn more about quaternion mathematics and how they are implemented in Sensor Fusion and Tracking Toolbox™, see Rotations, Orientation, and Quaternions. To learn more about conventions and coordinate systems in Sensor Fusion and Tracking Toolbox, see Orientation, Position, and Coordinate Convention.

## Functions

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 `quaternion` Create a quaternion array `ones` Create quaternion array with real parts set to one and imaginary parts set to zero `zeros` Create quaternion array with all parts set to zero `classUnderlying` Class of parts within quaternion `normalize` Quaternion normalization `randrot` Uniformly distributed random rotations
 `times, .*` Element-wise quaternion multiplication `mtimes, *` Quaternion multiplication `prod` Product of a quaternion array `minus, -` Quaternion subtraction `uminus, -` Quaternion unary minus `conj` Complex conjugate of quaternion `ldivide, .\` Element-wise quaternion left division `rdivide, ./` Element-wise quaternion right division `exp` Exponential of quaternion array `log` Natural logarithm of quaternion array `power, .^` Element-wise quaternion power
 `dist` Angular distance in radians `norm` Quaternion norm `angvel` Angular velocity from quaternion array `meanrot` Quaternion mean rotation `slerp` Spherical linear interpolation
 `rotateframe` Quaternion frame rotation `rotatepoint` Quaternion point rotation
 ```ctranspose, '``` Complex conjugate transpose of quaternion array ```transpose, .'``` Transpose a quaternion array
 `rotmat` Convert quaternion to rotation matrix `rotvec` Convert quaternion to rotation vector (radians) `rotvecd` Convert quaternion to rotation vector (degrees) `parts` Extract quaternion parts `euler` Convert quaternion to Euler angles (radians) `eulerd` Convert quaternion to Euler angles (degrees) `compact` Convert quaternion array to N-by-4 matrix
 `transformMotion` Compute motion quantities between two relatively fixed frames `enu2lla` Transform local east-north-up coordinates to geodetic coordinates `ned2lla` Transform local north-east-down coordinates to geodetic coordinates `lla2ned` Transform geodetic coordinates to local north-east-down coordinates `lla2enu` Transform geodetic coordinates to local east-north-up coordinates