Yksikkökvaternionen
Yksikkökvaternionen, often referred to as a unit quaternion, is a type of quaternion where the norm (or magnitude) is equal to one. A quaternion is a number system that extends complex numbers, with four components: one real part and three imaginary parts, typically represented as $a + bi + cj + dk$, where $i, j, k$ are the imaginary units satisfying $i^2 = j^2 = k^2 = ijk = -1$. For a unit quaternion $q = a + bi + cj + dk$, its norm is defined as $||q|| = \sqrt{a^2 + b^2 + c^2 + d^2}$. Therefore, for a unit quaternion, $a^2 + b^2 + c^2 + d^2 = 1$.
Unit quaternions are particularly important in three-dimensional geometry and computer graphics. They provide a computationally efficient