Quaternions: the Strange Numbers That Birthed Modern Algebra
I&#x27;ve found that the easiest way to understand quaternions is by visualizing them as scaled &quot;look&quot; or &quot;orientation&quot; vectors.<p>For example, if an airplane is oriented in the direction (x,y,z) at a rotation θ around that axis, then its rotation in quaternion form is cos(θ&#x2F;2)+x sin(θ&#x2F;2) i + y sin(θ&#x2F;2) j + z sin(θ&#x2F;2) k<p>Notice that the multiplications involving x, y, and z are just scaling the vector.<p>The other important thing to realize is that sin(θ&#x2F;2) is greater than or equal to zero in the interval [0, 2*pi]. So a quaternion is just a look vector where the magnitude of the vector is determined by the rotation around the look vector axis.<p>See this page for a useful picture: <a href="http:&#x2F;&#x2F;www.chrobotics.com&#x2F;library&#x2F;understanding-quaternions" rel="nofollow">http:&#x2F;&#x2F;www.chrobotics.com&#x2F;library&#x2F;understanding-quaternions</a>