Equations for the position to velocity (PPV) cubes were computed for a 3-D cube of density with its center (point P) at a given distance (d) from Sun (S). Here, by data convention, Y axis is along the line of site (SP).

For any pixel in the cube (point Q), the line of site SQ would then subtend an angle wrt the center (SP). Let Q' be the projection of Q on X-Y plane, therefore, SQ' has projections of x & y along the two axes.

We can then relate R0 (= CS = distance of Sun from Galaxy's center), R ( = distance CQ'), distance d (SP), and distance d' (SQ') through other quantities and angles (such as longitude= angle CSP).

The projection of relative velocity between S & Q' (due to galactic rotation) is added to the projections of the pixel velocities (vxx, vyy and vzz). Doing this for each pixel creates the cube "v_los". We sort the pixel values falling in different velocity bins, and make velocity maps of width 1 km/s.

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