Triaxial ellipsoid model and coordinate systems used in the triaxial analysis. The intrinsic coordinate system of the ellipsoid is denoted by dotted gray arrows ($x_1^{\mathrm{int}}$, $x_2^{\mathrm{int}}$, and $x_3^{\mathrm{int}}$), where $x_3^{\mathrm{int}}$ represents the major axis. The black arrows ($x_1^{\mathrm{obs}}$, $x_2^{\mathrm{obs}}$, and $x_3^{\mathrm{obs}}$) correspond to the observer’s coordinate system, where $x_3^{\mathrm{obs}}$ is aligned with the observer’s line of sight. In other words, an observer views the ellipsoid in the $-x_3^{\mathrm{obs}}$ direction. The three Euler angles (θ, φ, ψ) characterize the intrinsic coordinate system of the ellipsoid in relation to the observer’s coordinate system. The blue line represents the line of nodes, which is the intersection of the $x_1^{\mathrm{int}}-x_2^{\mathrm{int}}$ plane and the $x_1^{\mathrm{obs}}-x_2^{\mathrm{obs}}$ plane, and it is aligned with the vector $x_3^{\mathrm{int}}\times x_3^{\mathrm{obs}}$. The red ellipse denotes the projection of the ellipsoid on the sky plane, with l_p representing its semimajor axis. The dashed black line on the ellipse shows the projected major axis of the ellipsoid on the sky plane. The green ellipse is the projection of the ellipsoid onto the plane that is perpendicular to the sky plane, and l_los is the half size of the ellipse along the observer line of sight. See also Figs. 2 and 3 in Sereno et al. (2012).