Structural decomposition based on orbital properties demonstrated using Au-23-85-50 and compared with the truth. Four properties are used to decompose the galaxy: Circularity, λ_z; time-averaged radius, R; axis ratio, p_orb, in the x-y plane; and axis ratio, q_orb, in the x-z plane. The top panels display the true distributions while the bottom panels correspond to the model results. Left panels: Stellar orbit distributions of the entire galaxy in the λ_z–R phase space. We calculate the 1 kpc moving average of the cold orbit fraction f_cold (λ_z ≥ 0.8; 1 arcsec = 0.2 kpc) and define the dynamical bar length, R_bar, as the smallest radius where f_cold ≥ 0.5. Orbits with R ≤ R_bar are classified as bar+bulge components; those with R > R_bar are categorised as disc+halo components. The values of R_bar are indicated by the blue dashed lines and the annotations. Middle panels: Stellar orbit distributions for bar and bulge components in the λ_z–p_orb phase space. Orbits with λ_z ≤ 0.5 and p_orb ≥ 0.8 are assigned to the bulge; other orbits constitute the bar. The boundaries between the bar and bulge are shown by the blue dashed lines. Right panels: Stellar orbit distributions for disc+halo components in the λ_z–q_orb, in phase space. Orbits with λ_z ≤ 0.5 and q_orb, in ≥ 0.3 are categorised as the stellar halo; while the other orbits make up the disc. The boundaries between the disc and halo are shown by the blue dashed lines.