Figure 3 –

Centroid-boundary distance encoding of environmental geometry. A) left, top-down schematic view of the recording arena showing measurement of egocentric center-bearing and HD. right, egocentric center-bearing and HD are summed to compute allocentric center-bearing (α). This calculation can be reversed to compute the allocentric bearing of the animal’s location with respect to the centroid (1- α). B) left, top-down schematic view of a 120 × 120 cm square recording arena. Arrows pointing from the arena centroid to the boundary at specific allocentric bearings indicate measurement of centroid-boundary distance (CBD) along that angle. right, CBDs plotted as a function of allocentric bearing relative to the centroid. The result is a CBD signature that is unique to the shape and size of the arena. C-E) Same as B but for a 60 × 60 cm square, 120 × 60 cm rectangle, and 120 cm diameter circle, respectively. Note that while the arenas in B and C are both squares, they have unique CBD signatures because of their different sizes.