Fig. 1. Geometry of the system.

(A) A set of disks with diameter BL (body length) is considered. Each disk is propelled in the direction ψ_i with a velocity v_i(t). (B) A co-moving referential can be defined following the movement of the disk j. This referential is centered on the position of the disk, (x_j,y_j), and oriented so that the vertical axis is aligned with the direction ψ_j. The position of other objects can be recovered through their left-right (d_LR) and front-back (d_FB) distances relative to the disk j. ϕ represents the swiping angle. (C) Representation of the visible field of the pink disk through ray casting. The position of the eye is considered to be at the center of the disk with a fully circular point of view, i.e., no blind angles. (D) The projection of the visual field in two dimensions (2D) is given by a 1D function. On top, objects can be represented by their colors. However, on the bottom part, a binary visual field is given. It is not possible to distinguish individuals.