Figure 4 in Eigensurface analysis, ecology, and modelling of morphological adaptation in the falconiform humerus (Falconiformes: Aves)

Figure 4. Steps in the definition of eigensurface sampling grids as exemplified by the three scans of the proximal–dorsal surfaces of the humeri illustrated in Figure 3. The upper row shows the region selected for analysis. Point clouds of approximately 2000–3000 points representing this region were saved as ASCII text files along with separate files recording the boundary outline coordinates, points along a midline, and the coordinate positions of the two landmarks selected to orient the grid. Lower row: eigensurface form sampling grids. Each eigensurface grid is calculated by selecting a grid resolution (e.g. 10, 15, 20) and then interpolating that number of equally spaced semilandmark points along each half-outline (black) and along the surface trace of the chord joining the orientation landmarks (white). In this analysis a grid resolution of 10 was selected and the landmark chord oriented so that it traced the approximate position of the mid-line running from the humerus head down the centre of the shaft. Lateral or 'rib' chords are then drawn along the surface of the form such that each mid-line node is joined to a boundary outline node on either side. Equally spaced rib semilandmarks (grey) were then located along each of these rib chords with the number of semilandmarks used to quantify the shape of the chord being set iteratively as the number required to represent 95% of the length of the most contorted corresponding chord across the entire sample. This iterative procedure is identical to that used by MacLeod (1999) to sample boundary outline form in extended eigenshape analysis. The resulting grids quantify the geometric form of the surface of the humerus using an equal number of semilandmark points for each specimen in the sample and with each point being located in a position that corresponds topologically (relative to the grid point set as a whole) to all other points across the sample.