Coordinate Transformations and Trajectories

Quaternions, rotation matrices, transformations, trajectory generation

Navigation Toolbox™ provides functions for transforming coordinates and units into the format required for your applications. Use these functions to easily convert specific coordinates from one representation to the other.

Functions

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Axis-Angles

`axang2quat`	Convert axis-angle rotation to quaternion
`axang2rotm`	Convert axis-angle rotation to rotation matrix
`axang2tform`	Convert axis-angle rotation to homogeneous transformation

Euler Angles

`eul2quat`	Convert Euler angles to quaternion
`eul2rotm`	Convert Euler angles to rotation matrix
`eul2tform`	Convert Euler angles to homogeneous transformation

Quaternions

`quaternion`	Create quaternion array (Since R2019b)
`quat2axang`	Convert quaternion to axis-angle rotation
`quat2eul`	Convert quaternion to Euler angles
`quat2rotm`	Convert quaternion to rotation matrix
`quat2tform`	Convert quaternion to homogeneous transformation

Rotation Matrices

`so3`	SO(3) rotation (Since R2022b)
`rotm2axang`	Convert rotation matrix to axis-angle rotation
`rotm2eul`	Convert rotation matrix to Euler angles
`rotm2quat`	Convert rotation matrix to quaternion
`rotm2tform`	Convert rotation matrix to homogeneous transformation

Homogeneous Transformations

`se3`	SE(3) homogeneous transformation (Since R2022b)
`tform2axang`	Convert homogeneous transformation to axis-angle rotation
`tform2eul`	Extract Euler angles from homogeneous transformation
`tform2quat`	Extract quaternion from homogeneous transformation
`tform2rotm`	Extract rotation matrix from homogeneous transformation
`tform2trvec`	Extract translation vector from homogeneous transformation

Latitude, Longitude, NED, and ENU

`enu2lla`	Transform local east-north-up coordinates to geodetic coordinates (Since R2021a)
`lla2enu`	Transform geodetic coordinates to local east-north-up coordinates (Since R2021a)
`lla2ned`	Transform geodetic coordinates to local north-east-down coordinates (Since R2021a)
`ned2lla`	Transform local north-east-down coordinates to geodetic coordinates (Since R2021a)

Coordinate Conversions

`angdiff`	Difference between two angles
`cart2hom`	Convert Cartesian coordinates to homogeneous coordinates
`hom2cart`	Convert homogeneous coordinates to Cartesian coordinates
`trvec2tform`	Convert translation vector to homogeneous transformation

Trajectory Generation

`waypointTrajectory`	Waypoint trajectory generator (Since R2019b)
`kinematicTrajectory`	Rate-driven trajectory generator (Since R2019b)

Transformations

`se2`	SE(2) homogeneous transformation (Since R2022b)
`se3`	SE(3) homogeneous transformation (Since R2022b)
`so2`	SO(2) rotation (Since R2022b)
`so3`	SO(3) rotation (Since R2022b)
`plotTransforms`	Plot 3-D transforms from translations and rotations
`transformMotion`	Compute motion quantities between two relatively fixed frames (Since R2020a)

Visualization

`poseplot`	3-D pose plot (Since R2021b)
`PosePatch Properties`	Pose plot appearance and behavior (Since R2021b)

Blocks

Coordinate Transformation Conversion

Convert to a specified coordinate transformation representation

Featured Examples

Rotations, Orientation, and Quaternions

Reviews concepts in three-dimensional rotations and how quaternions are used to describe orientation and rotations. Quaternions are a skew field of hypercomplex numbers. They have found applications in aerospace, computer graphics, and virtual reality. In MATLAB®, quaternion mathematics can be represented by manipulating the quaternion class.

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