Z-axis (roll): \[ \left( \begin{array}{ccc} x' \\ y' \\ z' \\ 1 \end{array} \right) = \left( \begin{array}{ccc} \cos(\theta) & -\sin(\theta) & 0 & 0 \\ \sin(\theta) & \cos(\theta) & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array} \right) \cdot \left( \begin{array}{ccc} x \\ y \\ z \\ 1 \end{array} \right) \] X-axis (pitch): \[ \left( \begin{array}{ccc} x' \\ y' \\ z' \\ 1 \end{array} \right) = \left( \begin{array}{ccc} 1 & 0 & 0 & 0 \\ 0 & \cos(\theta) & -\sin(\theta) & 0 \\ 0 & \sin(\theta) & \cos(\theta) & 0 \\ 0 & 0 & 0 & 1 \end{array} \right) \cdot \left( \begin{array}{ccc} x \\ y \\ z \\ 1 \end{array} \right) \] Y-axis (yaw): \[ \left( \begin{array}{ccc} x' \\ y' \\ z' \\ 1 \end{array} \right) = \left( \begin{array}{ccc} \cos(\theta) & 0 & \sin(\theta) & 0 \\ 0 & 1 & 0 & 0 \\ -\sin(\theta) & 0 & \cos(\theta) & 0 \\ 0 & 0 & 0 & 1 \end{array} \right) \cdot \left( \begin{array}{ccc} x \\ y \\ z \\ 1 \end{array} \right) \] Common order of operations: \[ \left( \begin{array}{ccc} x' \\ y' \\ z' \\ 1 \end{array} \right) = \left[ translate \right] \cdot \left[ yaw \right] \cdot \left[ pitch \right] \cdot \left[ roll \right] \cdot \left( \begin{array}{ccc} x \\ y \\ z \\ 1 \end{array} \right) \]