Fig. 3. Constructing the odontophore and the prow. (A) Perspective view of a square containing a mid-sagittal outline of the odontophore and prow extracted from high-temporal-resolution magnetic resonance imaging (MRI). The prow seam and the line of widest extent (see D and E and text for definition) are indicated. A, anterior; D, dorsal; P, posterior; V, ventral. (B) Curve defining the medio-lateral dimension. The curve lies in the plane that contains the line of widest extent and is perpendicular to the mid-sagittal plane. The curve is constructed of four spline quadrants whose spline parameters are based on high-spatial-resolution MRIs of an anesthetized odontophore (see Fig. 2C,D and Table 1). The four anchor points for this curve at which the spline quadrants meet are defined as follows (each is indicated by a small circle): the posterior anchor point is the intersection of the line of widest extent with the mid-sagittal odontophore outline; the anterior anchor point lies along the line of widest extent, and its position is defined such that the width of the curve at the prow seam is equal to the fixed maximum prow width (see Table 1). The other two anchor points are midway between the prow seam and the posterior anchor point in the antero-posterior direction, and their medio-lateral position is iterated until the correct odontophore volume is achieved. (C) Example of one of the closed curves used in the construction of the odontophore mesh. The antero-posterior intersections of the planes of these curves are illustrated in Fig. 4C. Anchor points are indicated using circles. The dorsal and ventral anchor points are defined by the intersection of the plane of the curve with the mid-sagittal outline of the odontophore (A). The medio-lateral anchor points are defined by the intersection of the plane of the curve with a curve defining the medio-lateral width (B). (D) The tip of the prow is indicated by a grey circle. See Materials and methods for the algorithm that locates it along the anterior margin of the prow. (E) The line of widest extent passes through the tip of the prow. In the orientation shown, its angle is 44° counterclockwise from the line connecting the top of the radular surface and the tip of the prow. The top of the radular surface is defined in the reference frame in which the line connecting the tip of the prow and the bottom of the prow seam is vertical (represented by the vertical dashed line). (F) Construction of the prow. Each line indicated here represents a side view of a closed curve similar to that described in C. The portion of the curve above the line of widest extent is parallel to the prow seam. The portion of the curve below the line of widest extent is bent such that its antero-posterior position remains at the same percentage of the distance between the anterior margin of the prow and the prow seam as it had when it intersected the line of widest extent.

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