## 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). *r*_{h} and *r*_{v} 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*); *r*_{3D} denotes the radius of the circle that best fits **b**(*s*) itself.