Fig. 1. Illustration of the method used for deriving imposed- and self-translation. (A) Hypothetical experiment in which a crab is rotated on a disk (see text). The crab's transverse axis is denoted by an arrow on its body pointing to the homeward side. Numbered green open circles indicate the crab's position at each time point. The red circle indicates the final position of the crab if it had not moved (see text for details). (B) The experiment between times t₀ and t₁. The absolute translation vector (violet arrow) is digitized from video. The imposed translation vector (red arrow) is normal to the radius (red broken line) bisecting the crab's position at t₁ and t₂ (green open circles), and thus estimates the mean of all (unmeasured) imposed directions between the two discrete sampling times. It is the same length as the arc passing under the spot bisecting the crab's position at t₁ and t₂ (gray arc). The self-translation vector (blue arrow) is the vector subtraction of the imposed from the absolute translation vector; i.e. violet – red = blue. (C) Illustration of the imposed- and self-translation vectors (red and blue, respectively) for each step in the path shown in A. Green circles correspond to those in A.