What is the mathematical definition of a rotation in 3D space?
A rotation in 3D space is a three-dimensional transformation that describes an object turning around an axis by a certain angle. The mathematical definition of a 3D rotation involves a quaternion, a four-dimensional vector that describes an object’s orientation in 3D space.
A quaternion is typically written as q = w + xi + yj + zk, where w, x, y, and z are the components of the quaternion, and i, j, and k are special imaginary numbers.
These components can be thought of as an axis of rotation and an angle to rotate about the axis. In other words, giving the components of a quaternion specifies a rotation in 3D space.
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