Schematics illustrating four possible choices of horizontal plane and the consequences of varying head pitch on the mathematical description of basepoint coordinates and whisker orientation.

<p>(A) The average whisker row plane is found by averaging the planes of best fit for each individual whisker row across left and right sides of the face. This plane is defined as “horizontal” in the present work. (B) Connecting the eye corners and nose yields an ~+12° offset from the average whisker row plane, tilting the rat head slightly upward. (C) The bregma-lambda plane is offset from the average whisker row plane by ~-8°, pitching the rat head slightly downward. (D) The semi-circular canal plane is offset by ~-38.5°, tilting the rat head substantially downward. (E) The left panel shows the angular basepoint coordinates (θ_bp, φ_bp) of two example whiskers (B2, D6) when the average row plane is defined as the horizontal x-y plane. The coordinate for B2 is (-21.5°, 22.3°) and the coordinate for D6 is (27.6°, -15.9°). The pale purple horizontal line at φ_bp = 0° represents the average row plane. The x-axis is also colored purple to highlight that it is parallel with the average row plane. The right panel shows the angular coordinates (θ_bp, φ_bp) of the same two whiskers (B2, D6) when the semi-circular canal plane is defined as horizontal. The coordinate for the B2 whisker is now (-2.2°, 30.2°) and the D6 whisker coordinate is now (13.1°, -29.5°). The pale green horizontal line indicates the semi-circular canal plane. The x-axis is also shown in green to highlight that it is now parallel to the semi-circular canal plane. Values in image have been truncated for visual clarity. (F) The left panel shows the angles of emergence for the C3 whisker, projected into the x-y plane (blue) and the x-z plane (red). These projection angles are denoted as θ_proj and φ_proj. In this panel, the average whisker row plane is defined as the horizontal plane, and the blue and red vectors represent projections of the proximal (approximately linear) portion of the whisker. The right panel illustrates the same angles of emergence when the semi-circular canal plane is defined as the horizontal plane. The redefined x-y plane is shown in green and the x-z plane in orange. New projection angles for the proximal, approximately linear portion of the whisker, are illustrated by the green and orange vectors. Again, although the relative orientation of the whisker with respect to all other facial features remains constant, the projection angles describing the orientation of that whisker are affected by choice of head pitch.