Projections of a paraboloid shape from the natural star frame to the observer frame. Panel a) shows a cut through the paraboloid in the plane x = X = 0 defined by the star proper motion vector V_∗ and the line of sight (Z axis pointing away from the observer). Point A is the real apex of the parabola, A′ is the apparent apex as seen by the observer, A′′ the projection of A′ on the Y axis, and C the intersection of the front side of the parabola with the line of sight. Panel b) shows the paraboloid apparent shape as seen in projection in the XY plane of the sky.