Motion/Pursuit Law on Invariant Circles (Visual Depth Perception 4)
This Demonstration computes the motion/pursuit law in the two-dimensional horizontal "fixation plane" of the eyes. The observer is looking mainly at F on the vertical axis, but also sees D as she translates to the right at 6.5 cm/sec (interocular distance per second). The distractor can be moved off the axis around the time zero invariant circle.
We do not know a theoretical explanation for the rough approximation of the peak motion/pursuit law by the 2D relative distance, but this Demonstration compares , , and the 2D signed relative distance, . It also lets you vary time and compare the motion/pursuit law at other times.
The motion/pursuit ratio at is constant on circles passing through the eye node at time zero and distractor with diameter on the axis. (These circles are similar to the invariant circles for binocular disparity, but slightly different.)
This means that the time zero motion/pursuit law is NOT an especially good indicator of the relative distance between the two-dimensional distractor and fixate, , because you can move quite far from F on this circle with no change in the quantity . If we take the translation of the observer into account, we can show that the peak value of the motion/pursuit law is a good indicator of the relative distance in two dimensions. (It is also likely that the changing value of the motion/pursuit ratio is a cue that the brain could use.)
The Demonstration, "Motion/Pursuit Law in 2D (Visual Depth Perception 3)" (see Related Links) contains additional details.