Left: theoretical average surface brightness distribution as a function of projection factor μ integrated over the spectrum between 3400 Å and 3500 Å, computed using our “standard” numerical resolution for an arbitrary snapshot of the 3D model of HD 189733 (crosses), and least-squares fits of the Claret (2000) nonlinear law (solid line) and a linear law (dotted line). The gray-shaded area indicates the central part of the stellar disk that is not reached during the transit. Right: relative deviation of spline interpolations of theoretical limb darkening computed with N_φ = 8 direction angles (solid line) and with the full horizontal resolution of N_x = N_y = 240 grid points (dotted line) from the interpolated “standard” setting.