Description of a whisker in terms of 3D kinematic and 3D shape parameters.
A) Azimuth (θ), elevation (φ) and roll (ζ) angles. These angles are defined with respect to the tangent to the Bezier curve b(s) describing the whisker, at s = 0. Azimuth describes rotation about the vertical (dorso-ventral) axis through s = 0; elevation describes rotation about the horizontal (anterior-posterior) axis through s = 0; roll describes rotation about the x′ axis, defined in panel B. B) Left. Whisker-centric coordinate frame with origin at s = 0 (Eqs 9–11). The x′ axis is tangent to b(s) at s = 0; the y′ axis is the direction in which b(s) curves; the z′ axis is orthogonal to the x′−y′ plane. Middle. Components of moment in the whisker-centric coordinate frame. Right. 2D and 3D whisker curvature (Eqs 13–15). rh and rv denote the radii of the circles that best fit the projection of b(s) into the horizontal and vertical image planes respectively (at a given point s); r3D denotes the radius of the circle that best fits b(s) itself.