convert... And then use the basis to log quaternion conversion... Align Normal Directly Or This is the direct computation to result with a log quaternion; compute the above result vector and then... This is the angle These partial products are used below... Compute the normalized rotation vector (axle of rotation)... and finally compute the resulting log quaternion. Conversion from axis-angle This assumes the input axis is normalized. If there is 0 rotation, result with See also Euler filter Orientation (geometry) Rotation around a fixed axis Three-dimensional rotation operator References Further reading External links EuclideanSpace has a wealth of information on rotation representation Q36. How do I generate a rotation matrix from Euler angles? and Q37. How do I convert a rotation matrix to Euler angles? — The Matrix and Quaternions FAQ Imaginary numbers are not Real – the Geometric Algebra of Spacetime – Section "Rotations and Geometric Algebra" derives and applies the rotor description of rotations Starlino's DCM Tutorial – Direction cosine matrix theory tutorial and applications. Space orientation estimation algorithm using accelerometer, gyroscope and magnetometer IMU devices. Using complimentary filter (popular alternative to Kalman filter) with DCM matrix. Rotation Euclidean symmetries Orientation (geometry) Rigid bodies mechanics