Projection of velocity (v_gal) from NGC 1068 coordinates (primed) to sky coordinates (unprimed). The primed frame results from a i = 41° inclination rotation along the line of sight (from the negative z-axis to the z′-axis) and a PA = 289° rotation around z′-axis. The x′-axis aligns with the minor axis of the CND, matching the reference azimuthal direction (θ′₀), with the 90° difference between x′ and y′-axes corresponding to the difference between PA and the θ′₀ direction. The primed system follows a rightward primary axis convention, while the sky frame follows a northward reference. The PA reference axis is the x-axis after inclination rotation. The brown ball marks the molecular gas region, with outflow velocity v_gal assumed to lie in the CND plane, directed radially from the AGN (red star). It decomposes as v_outcos(θ) along x′-axis and v_outsin(θ) along y′-axis, where θ is measured from x′-axis. Using Eq. (8), v_gal is projected to sky velocity v_sky, decomposed into the observed radial velocity v_LOS and a transverse component (purple arrow), which further splits into v_x and v_y.