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Coordinate Transformations

Quaternions, rotation matrices, transformations

Robotics System Toolbox™ provides functions for transforming coordinates and units into the format required for your applications. To learn more about the different coordinate systems, see Coordinate Transformations in Robotics.


se2SE(2) homogeneous transformation (Since R2022b)
se3SE(3) homogeneous transformation (Since R2022b)
so2SO(2) rotation (Since R2022b)
so3SO(3) rotation (Since R2022b)
quaternionCreate quaternion array


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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
quat2axangConvert quaternion to axis-angle rotation
quat2eulConvert quaternion to Euler angles
quat2rotmConvert quaternion to rotation matrix
quat2tformConvert quaternion to homogeneous transformation
rotm2axangConvert rotation matrix to axis-angle rotation
rotm2eulConvert rotation matrix to Euler angles
rotm2quatConvert rotation matrix to quaternion
rotm2tformConvert rotation matrix to homogeneous transformation
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
angdiffDifference between two angles
cart2homConvert Cartesian coordinates to homogeneous coordinates
hom2cartConvert homogeneous coordinates to Cartesian coordinates
trvec2tformConvert translation vector to homogeneous transformation
plotTransformsPlot 3-D transforms from translations and rotations