Coordinate Transformations and Trajectories

R2026b

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

expand all

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
`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
`lla2enu`	Transform geodetic coordinates to local east-north-up coordinates
`lla2ned`	Transform geodetic coordinates to local north-east-down coordinates
`ned2lla`	Transform local north-east-down coordinates to geodetic coordinates

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
`kinematicTrajectory`	Rate-driven trajectory generator

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

Visualization

`poseplot`	3-D pose plot
`PosePatch Properties`	Pose plot appearance and behavior

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.

Open Script