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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Initialization and Convenience Functions

`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

Mathematics

`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

Metrics and Interpolation

`dist`	Angular distance in radians
`norm`	Quaternion norm
`angvel`	Angular velocity from quaternion array
`meanrot`	Quaternion mean rotation
`slerp`	Spherical linear interpolation

Rotations

`rotateframe`	Quaternion frame rotation
`rotatepoint`	Quaternion point rotation

Array Manipulation

`ctranspose, '`	Complex conjugate transpose of quaternion array
`transpose, .'`	Transpose a quaternion array

Representation Conversion

`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

Coordinate Transformation

`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