Later Hermann von Helmholtz and Ewald Hering worked out the exact shape of the horopter almost at the same time. Their descriptions identified two components for the horopter for symmetrical fixation closer than infinity. The first is in the plane which contains the fixation point (wherever it is) and the two nodal points of the eye. The geometric locus of horopteric points in this plane takes the form of the arc of a circle (the Vieth-Müller circle) going from one nodal point to the other in space, passing through the fixation point. The second component is a line (the Prévost–Burckhardt line) which is perpendicular to this arc in the median plane, cutting it at the point midway between the two eyes (which may, or may not, be the fixation point). This horopter geometry of a circle in the fixation plane and a perpendicular line remains approximately fixed relative to the eye centers as long as the eyes are fixating somewhere on these two lines. When the eyes are fixated anywhere off these two lines, the theoretical horopter takes the form of a twisted cubic passing through the fixation point and asymptoting to the two lines at their extremes. (Under no conditions does the horopter become either a cylinder through the Vieth-Müller circle or a torus centered on the nodal points of the two eyes, as is often popularly assumed.) If the eyes are fixating anywhere at infinity, the Vieth-Müller circle has infinite radius and the horopter becomes the two-dimensional plane through the two straight horopter lines.