Geometrical definitions used by the code. See van der Marel & Cioni (2001), and van der Marel et al. (2002).

Fig 2, van der Marel et al. (2002)

Fig 3, van der Marel et al. (2002)

• Line of nodes: intersection of the rotated galaxy plane (x', y', z') and the sky plane (x, y, z). Formally, it is the x' axis.

• Position angle of the line of nodes (\Theta): counterclockwise rotation around the z axis, measured form the y axis (North). \Theta = \theta - 90º, ie: \theta is measured from the x axis (West)

• Inclination (i): clockwise rotation around the new x' axis. It is the angle between the (x, y)-plane of the sky and the (x', y')-plane of the galaxy disk.

Main function. Reads input data, obtains the angles for each method, and produces the final plots.

Read input data for both galaxies.

Reads all the parameters needed to process the data.

1. inc_PA_grid()

   Define a grid of (i, theta) angles.

2. angles2Plane()

   Convert each pair of (i, theta) angles to its "plane form": ax + by + c*z + d = 0.

   1. gal_theta()

      Convert position angle 'Theta' (N-->E) to 'theta' (W-->E).

Process all data.

1. dist2CloudCenter()

   3D distance between cluster-galaxy center and its error, in parsec.

   1. MCs_data()

      Read fixed data for each galaxy (center, distance, error in distance.

   2. dist_err_mag_2_pc()

      Convert the error in distance modulus to an error, in parsec.

   3. dist_err_2_pts()

      Error for the cluster-galaxy center distances, in parsec.

2. dist_filter()

   Filter clusters based on their projected angular distances ('rho').

   1. get_rho_phi()

      Projected angular distance cluster-galaxy center, and position angle of cluster.

3. i_PA_DeprjDist()

   Deprojected distance values for each (i, PA) point in the defined grid.

   1. get_deproj_dist()

      1. vdm_2001_dep_dist_kpc()

         Use Eq. (8) from van der Marel & Cioni (2001).

4. xyz_coords()

   Coordinates of filtered clusters in the (x,y,z) system.

5. Methods

   1. m1_ccc_map
      1. ccc Concordance correlation coefficient between deprojected distances obtained using ASteCA's distances and the van der Marel's equations.
   2. interp_dens_map
   3. m2_fix_plane_perp_dist For each (i, theta) pair, calculate the mean of the perpendicular distances of all clusters to that plane.
   4. interp_dens_map
   5. m3_min_perp_distance
      1. perp_error
   6. interp_dens_map
   7. get_angles Extract the best fit angles from all the (i, theta) values tested by the methods 1 and 2. For method 3, call function below.
      1. angle_betw_planes Transform the (a, b, c, d) plane parameters for the best fit found by Method 3, into (i, theta) angles.
   8. ccc_sum_d_for_best_fit
      1. get_deproj_dist
      2. ccc
      3. perp_error
   9. monte_carlo_errors
      1. draw_rand_dep_dist
      2. draw_rand_dist_mod
   10. cov_ellipse

Produce final plots.

Subramanian & Subramaniam (2015) (SMC), Subramanian & Subramaniam (2010) (LMC)