Axis-angle to Quaternion 변환

Axis angle을 Quaternion으로 변환해보자 !

수식

\[\begin{align} & qx = ax \; sin(\frac{angle}{2}) \\ & qy = ay \; sin(\frac{angle}{2}) \\ & qz = az \; sin(\frac{angle}{2}) \\ & qw = con(\frac{angle}{2}) \\ \end{align}\]

\(where, \\\)
1) the axis is normalized: \(ax^2 + ay^2 + az^2 = 1 \\\)
2) the quaternion is also normalized : \(qw^2 + qx^2 + qy^2+qz^2=1 \\ cos(\frac{angle}{2})^2 + ax^2 \; sin(\frac{angle}{2})^2 + ay^2 \; sin(\frac{angle}{2})^2+ az^2 \; sin(\frac{angle}{2})^2 = 1 \\\)