Almost spherical model of ε Ori based on CFHT spectroscopy. Hydrogen Balmer lines were fitted using 1443 data points, excluding H_α and H_β, which are ‘filled’ by wind-induced emission. An interstellar calcium 3968 Å for H_ε was masked. The best fit resulted in χ_SPE² = 1770. Free parameters were P_rot = 4.551 d, T = 25 037 K, log g = 3.016, i = 21.40 deg, and γ = 25.00 km s⁻¹. Other parameters were fixed and set according to interferometry. The derived parameters were v sin i = 111 km s⁻¹ and v = 305 km s⁻¹. The dotted lines show laboratory wavelengths, while the solid vertical lines indicate the Doppler-shifted line centres, corresponding to the resulting γ. The teal circles denote the points that contributed to χ² with values greater than 10. This model explains reasonably well the Balmer lines, with a few systematics remaining in H_ε, H_η, possibly due to different metal abundances. The temperature was constrained, and log g was slightly adjusted. However, due to the difference in inclination (i = 21 vs 62 deg), the interferometric model would become worse, with χ_VIS² = 16.04. The fit of He I lines is given in Fig. C.5.