Sales Toll Free No: 1-800-481-2338

# Rotation Matrix to Quaternion

TopRotation matrix is normally used in linear Algebra. It can be defined as a matrix which can be used to find rotation in Euclidean space. As following matrix will rotate the points in anticlockwise direction by an angle 'θ' about the origin in Cartesian plane of Cartesian coordinate system.

Orientations and rotations of objects in 3D are represented by Unit quaternions. For this orientation Euler angles are not suitable since they are not easier as compared to unit quaternions in formulating problem of gimbal lock.
Unit quaternions are more efficient and stable as compared to that of rotation matrices.
Unit quaternions has use in field of computer graphics, robotics molecular dynamics and orbital mechanics of satellites. If we want to represent the rotation then unit quaternions can be called rotation quaternions. Rotation quaternions are also known as versors.
Let’s try to understand Rotation Matrix to quaternion conversion and vice versa. When unit quaternions are used to show an structure or orientation, they can be called as orientation quaternions. Orientation quaternions can also be stated as attitude quaternions. If we want to represent any rotation in 3D space then there are two parameters mainly required which are: 1) Axis vector and 2) Angle of rotation.
Quaternion rotation can be constructed using the formula:
q = exp 1/2 (θ) (pxi + pyi + pzi) = cos (½) θ + (pxi + pyj + pzj) sin (½) θ,
Where 'θ' is defined as angle of rotation and (px, py, pz ) is the rotation vector that represents the Axis of Rotation. Here for unit quaternion q = (m, a, b, c), equivalent left handed 3×3 rotation matrix will be:

Above matrix is showing a conversion from quaternion to a 3×3 rotation matrix.