PURPOSE. To provide an analytical geometric representation of the vertical horopter based on known empirical data. METHOD. This purely theoretical study utilizes methods of analytic geometry to model the vertical horopter for the most general case.
RESULTS. For the most general case, the vertical horopter does not pass through the feet of the observer. However, it passes through a point Q on the normal to the horizontal horopter. This point Q is obtained in terms of the direction cosines of the vertical horopter. Conversely, if we know Q from experiments, we can determine the direction cosines. We have also derived the expressions for the polar and azimuthal angles subtended at each eye with respect to the point of fixation by a point on the vertical horopter. The experimental measurements of these angles can provide us with equations of the vertical horopter. A functional expression for the tilt of the horopter as a function of fixation distance is also derived.
CONCLUSIONS. To the best of our knowledge, expressions for the vertical horopter analogous to the analysis of the horizontal horopter have not been derived. This model can be used to analyze the vertical horopter.