Yksikkökvaternioni

Yksikkökvaternioni, also known as a unit quaternion, is a type of quaternion where the norm (or magnitude) is equal to one. A quaternion is an extension of complex numbers, typically represented as q = a + bi + cj + dk, where a, b, c, and d are real numbers, and i, j, and k are imaginary units. The norm of a quaternion q is calculated as |q| = sqrt(a^2 + b^2 + c^2 + d^2). For a unit quaternion, this value is always 1.

Unit quaternions are particularly useful in representing rotations in three-dimensional space. Unlike Euler angles, which can suffer from gimbal lock, unit quaternions provide a smooth and unambiguous way to describe orientations and rotations. A unit quaternion can be thought of as encoding an axis of rotation and an angle of rotation. The product of two unit quaternions results in another unit quaternion, allowing for the composition of rotations.

The inverse of a unit quaternion is also a unit quaternion. Specifically, for a unit quaternion q, its inverse q⁻¹ is equal to its conjugate q* (where q* = a - bi - cj - dk). This property simplifies calculations involving rotations, such as reversing a rotation. Due to their efficiency and robustness, unit quaternions are widely employed in computer graphics, robotics, aerospace engineering, and physics.