Convention for observer angular position and AMR grid rotation. The third dimension (z axis) is dropped as it is left unchanged during our coordinate transformation. The observer is at (x, y) = (0, 0) and the galaxy center at (x_AMR, y_AMR) = (0, 0). The AMR grid is rotated clockwise by ϕ_⊙ about the galaxy center and then shifted at (x, y) = (8, 0) to make the circular excursion of the observer.