Supplementary Methods.

Fig A in S1 Text. Related to Fig 1. Diagram of the overall modeling approach. Within the gray box, the subscript “wobj” has been omitted from the geometric coordinates for brevity. Fig B in S1 Text. Related to Fig 3. The whisker and contact point location are shown in whisker-centered coordinates. A: In whisker-centered coordinates, the origin is placed at the whisker base, and the x-axis is collinear with the proximal region of the whisker. The proximal 70% of the whisker (which is close to planar) is adjusted to lie as close as possible to the x-y plane. The intrinsic curvature of the whisker points the whisker tip in the positive y-direction. B: The whisker-object (“wobj”) contact point location in whisker-centered coordinates is given by the coordinates rwobj, θwobj, and φwobj. The variable rwobj is the linear distance from the origin to the contact point location. θwobj, is the azimuthal angle of the contact point from the x-axis, and φwobj is the elevation angle of the contact point measured from the x-y plane. Fig C in S1 Text. Related to Figs 4 and 5. This figure provides a step-by-step explanation for how errors in the peg reconstruction (Figs 4 and 5 of main text) result from limitations in mapping resolution. The regions of the reconstructions with the largest error are those where Fx and MB are small. These regions correspond to points at large radial distances or points generated by small deflections. (A) This subplot illustrates the identical solid as shown in Fig 3D of the main text. The solid represents the mapping of Fx, MB, MD to rwobj. A vertical plane (red) is shown cutting through the solid at MD = 3π/2, and this slice of the solid is depicted in subplot (B). (B) This subplot shows the slice of the solid from (A) indicated by the red plane. Because the “solid” in (A) is represented by a series of monochromatic surfaces, the slice appears to be composed of different colored lines. Each line represents contact points at a single radial distance. In the lower-right hand corner of the figure, the lines are spaced far apart, indicating that the different radial distances are separated by large Fx and MB increments. In contrast, in the upper-left corner, the lines are spaced closely together, indicating that any small error in Fx or MB will result in a large error in rwobj. Note that this region includes all of the high values of rwobj, indicating that any contact points with a high rwobj are susceptible to large errors. The inset in the bottom-left corner shows an expanded view of this region. Inset x-axis limits: [0, 5]; inset y-axis limits: [-0.25, 0.05]. (C) This subplot shows the same lines as subplot (B) except the color map indicates mapping error. As expected, the region where resolution demands are high have larger errors. (D) The same solid as in (A), but with a colormap that indicates mapping error, and a “flipped” MB axis to better reveal the regions of high and low error. Layers are semi-transparent to aid with visualization. Table A in S1 Text. Related to Fig 3. A tabulation of the uniqueness for all 20 mappings. Boxes marked “All” indicate that the mapping is unique for the entire contact point space. Boxes marked “ELD” indicate that the mapping is unique only after excluding large deflections. Boxes marked “CF or “CB” indicate that the mapping is unique when only concave forward (CF) or concave backwards (CB) contact points are included. A mapping labeled “ELD CF” or “ELD CB” means that the mapping is unique only when concave forward or concave backwards are considered and large deflections are excluded. Some boxes include a forward slash and give multiple readings. This notation indicates that the mapping was unique for multiple conditions. For example, the way to read mapping 12 is that the mapping is unique if it is known whether the points are concave backwards or concave forward, provided large deflections are excluded. The way to read mapping 6 is that it is unique either if large deflections are excluded, or if only concave backwards points are considered. The mappings with boxes marked “not unique” had no well-defined regions of uniqueness. Two of the mappings are marked with an asterisk, indicating that they are non-unique specifically when the contact points are in the x-y plane, where Mx is always 0. (PDF)