ühikukvaterniooni
An ühikukvaternioon, or unit quaternion, is a quaternion with a magnitude of one. Quaternions are an extension of complex numbers, with the form a + bi + cj + dk, where a, b, c, and d are real numbers and i, j, and k are imaginary units satisfying i^2 = j^2 = k^2 = ijk = -1. The magnitude of a quaternion q = a + bi + cj + dk is defined as |q| = sqrt(a^2 + b^2 + c^2 + d^2). Therefore, an ühikukvaternioon satisfies the condition a^2 + b^2 + c^2 + d^2 = 1.
Ühikukvaternioonid are particularly useful in three-dimensional space for representing rotations. A unit quaternion can uniquely represent