pöördekvaternione

Pöördekvaternione refers to a specific application of quaternions in mathematics and computer graphics for representing rotations in three-dimensional space. Quaternions are an extension of complex numbers, consisting of a scalar part and a three-dimensional vector part. A unit quaternion, meaning a quaternion with a magnitude of one, can be used to parameterize a rotation.

A rotation in 3D space can be described by an axis of rotation and an angle of rotation. A unit quaternion representing this rotation can be constructed using the angle and the components of the normalized rotation axis. Specifically, if the axis of rotation is a unit vector (x, y, z) and the angle of rotation is theta, the corresponding quaternion q can be expressed as q = cos(theta/2) + (x*i + y*j + z*k)*sin(theta/2), where i, j, and k are the quaternion units.

To rotate a vector v using a quaternion q, the operation is performed as v' = q * v * q_conjugate, where v is treated as a pure quaternion (0 + v) and q_conjugate is the quaternion with the scalar part unchanged and the vector part negated. This method of rotation offers several advantages over other techniques like Euler angles or rotation matrices, including avoiding gimbal lock and being computationally efficient for composing rotations. They are widely used in fields such as robotics, aerospace engineering, and video game development for smooth and accurate 3D transformations.