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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.


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axang2quatConvert axis-angle rotation to quaternion
axang2rotmConvert axis-angle rotation to rotation matrix
axang2tformConvert axis-angle rotation to homogeneous transformation
eul2quatConvert Euler angles to quaternion
eul2rotmConvert Euler angles to rotation matrix
eul2tformConvert Euler angles to homogeneous transformation
quaternionCreate quaternion array (Since R2019b)
quat2axangConvert quaternion to axis-angle rotation
quat2eulConvert quaternion to Euler angles
quat2rotmConvert quaternion to rotation matrix
quat2tformConvert quaternion to homogeneous transformation
so3SO(3) rotation (Since R2022b)
rotm2axangConvert rotation matrix to axis-angle rotation
rotm2eulConvert rotation matrix to Euler angles
rotm2quatConvert rotation matrix to quaternion
rotm2tformConvert rotation matrix to homogeneous transformation
se3SE(3) homogeneous transformation (Since R2022b)
tform2axangConvert homogeneous transformation to axis-angle rotation
tform2eulExtract Euler angles from homogeneous transformation
tform2quatExtract quaternion from homogeneous transformation
tform2rotmExtract rotation matrix from homogeneous transformation
tform2trvecExtract translation vector from homogeneous transformation
enu2llaTransform local east-north-up coordinates to geodetic coordinates (Since R2021a)
lla2enuTransform geodetic coordinates to local east-north-up coordinates (Since R2021a)
lla2nedTransform geodetic coordinates to local north-east-down coordinates (Since R2021a)
ned2llaTransform local north-east-down coordinates to geodetic coordinates (Since R2021a)
angdiffDifference between two angles
cart2homConvert Cartesian coordinates to homogeneous coordinates
hom2cartConvert homogeneous coordinates to Cartesian coordinates
trvec2tformConvert translation vector to homogeneous transformation
waypointTrajectoryWaypoint trajectory generator (Since R2019b)
kinematicTrajectoryRate-driven trajectory generator (Since R2019b)
se2SE(2) homogeneous transformation (Since R2022b)
se3SE(3) homogeneous transformation (Since R2022b)
so2SO(2) rotation (Since R2022b)
so3SO(3) rotation (Since R2022b)
plotTransformsPlot 3-D transforms from translations and rotations
transformMotionCompute motion quantities between two relatively fixed frames (Since R2020a)
poseplot3-D pose plot (Since R2021b)
PosePatch PropertiesPose plot appearance and behavior (Since R2021b)


Coordinate Transformation ConversionConvert to a specified coordinate transformation representation