Fig. 2. The odontophore-centric kinematic model. (A) Superellipse function, which is used to create curved surfaces whose convexity or flatness varies with the value of a single parameter, n. The behavior of the function at several values of n is shown. (B) Extracting the midsagittal outline of the radula/odontophore from magnetic resonance (MR) images. With the images rotated such that the radular stalk is vertical, the anterior, posterior, dorsal and ventral extrema of the radula/odontophore are determined (horizontal and vertical lines). For each quadrant, four points on the surface of the curve are selected (open circles, shown only for the antero-ventral quadrant). Best-fit superellipse curves are found using these control points (see Materials and methods). In the antero-dorsal quadrant, the point at which the presumed long axis of the I7 muscle (diagonal line) intersects the radular surface is determined (filled circle). (C—E) Three-dimensional renderings (orthographic projection) of the resulting odontophore-centric model with the right half of the odontophore cut away to reveal the radular stalk (realistically reconstructed from high-spatial-resolution MR images) and the I7 muscle. All structures are represented as isosurfaces composed of triangles. (C) Mediolateral view with the four superellipse quadrants a—d. (D) Antero-posterior view. Curves e and f are ellipses (n=1.0) because there are no data available to determine their true shape with high temporal resolution. (E) Dorso-ventral view. Curves g and h are assumed to be ellipses (n=1.0), as in D. Volumetric databases are created from each radula/odontophore isosurface by stepwise slicing along the antero-posterior axis, as in the radula-centric model (Fig. 1D).

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