Fig 1 -

(a) A schematic depiction of a neighbor’s observed geometrical features and notation used. The bearing angle β_j defines the angle between the heading of the focal agent (v_o) and the line of sight (LOS, as defined in the text). The circle represents the idealized sensor of the focal agent. The subtended angle α_j is defined as the angle between the edge rays directed towards the extremities of the neighbor. The distance from the focal agent to the center of neighbor j is denoted r_j. The neighbor’s velocity v_j, is composed of two orthogonal components: the radial component v_j,r is parallel to LOS, and the tangential component v_j,t is perpendicular to LOS. The unit vectors are equal to v_j,r, v_j,t but with magnitude fixed to 1; they are not shown in the figure. (b) Geometry of finding the subtended angle α_j. Edge rays are denoted with green lines. Edge rays pass at two corners of the neighboring agent, and the segment between those points we define as the ‘effective edge’ d (here, d_A for neighbor A, d_B for neighbor B, etc.). Depending on the relative orientation of the neighbor with respect to the focal agent, the effective edge may be either the neighbor’s diagonal (see neighbor A), its shorter side (neighbor B), or its longer side (neighbor C).