Rotating a point with homogeneous coordinates \((x, y, w)\) around the origin by an angle \(\alpha\) can be achieved using
\[ \begin{bmatrix}
\cos\alpha & -\sin\alpha & 0 \\
\sin\alpha & \cos\alpha & 0 \\
0 & 0 & 1 \\
\end{bmatrix}
\cdot
\begin{bmatrix}
x \\
y \\
w \\
\end{bmatrix}\]