As shown in Figure 2, the length of OP in the triangle COP is , where r = |CP| is the radius of the circle, and r₀ is the length |CO|. (Without loss of generality, in Beghi et al. (1991a), the origin O of the Oxy system is positioned half way between the center of the circle, C, and the off-centered dot E. The same convention is adopted here.) Hence, the speed of point P is (the 4th equation from bottom left, p. 429):

The remainder of this section assigns the 3-D coordinates of the circle and dot without mathematical reasoning. So there are no derivations to be analyzed. Still, the introduction of v_z(P) makes the circle non-planar in 3-D due to the nonlinearity of Equation 14 (as in the case of the rotating bar). This contradicts the prediction of the model, e.g., in Figure1b of Beghi et al. (1991a), and of the empirical perceptual result. Since the alternative method in Beghi et al. (1991a) claims that the circle remains planar in 3-D (p. 430), which contradicts Equation 14, and since the alternative method claims to yield the same result, it is self contradictory.