Line profiles for a ring geometry simulated with RELXILL. We display the geometric parameters of the ring in terms of spherical radii, r, and polar angles, θ. The parameters are uniquely related to height and ring radius through Eq. (4). For ease of comparison, we also convert these values to heights and radii in Table 1. (a) Varying polar angle of the primary source, θ, for two spherical radii, r = 3r_g (dashed lines) and r = 9r_g (solid lines), with a = 0.998. (b) Varying the spherical radius of the primary source, r, with two polar angles of the primary source, θ = 30° (solid lines) and θ = 0° (dashed lines, the lamp post case), with a = 0.998. (c) Varying the BH spin, a, for a source spherical radius fixed at ISCO value, r = r_ISCO, and θ = 60°. ISCO radii are 1.24r_g, 6r_g, 9r_g for a = 0.998, 0.0, −0.998, respectively. To convert the quantities (r, θ) to (h, x), we provide the Table 1. All lines are normalized to have the same integrated photon flux. The photon index is Γ = 2 and the inclination to the observer is i = 30°.