(A), (B) Earth-horizontal azimuth model, illustrating the distortion produced. The larger the tilt angle of the head away from the earth-horizontal surface, the larger the distortion between egocentric and allocentric reference frames. (C) Head-horizontal (yaw-only) azimuth model, with the compass attached to the head horizontal plane. After completing a 3D trajectory and returning to surface n∘1, the head-fixed compass (small red compass on surface n∘1) is no longer consistent with its orientation at the beginning of the trajectory (large compass on surface n∘1). Therefore, a purely egocentric azimuth compass can’t track head orientation during motion in 3D.