We digitized a skull of an extant species; split the specimen into several different configurations; linearly shortened each splitting configuration from several different angles; reconstructed the distorted pieces on both the original skull and a deformed version of the original skull; and measured the fit and symmetry of the resulting reconstructions. Each step is explained below.

We digitized the skull of a Woolly Monkey (Lagothrix lagotricha), which had a principal component axis length of 10 cm, with a Minolta Non-contact 3-D Digitizer Vivid 910. Next, using Rapidform 2004 3-D Visualization and Manipulation software, we split the skull into four different configurations. The splitting regimes were dictated by the construction of an artificial 3-D Cartesian coordinate plane within the skull with its center at the center of volume of the skull. The Y-axis connected the top and the bottom of the skull, the Z-axis connected the dorsal and the ventral portions, and the X-axis connected the two sides of the skull. The first splitting group divided the skull into halves on each of these axes with an end result of eight pieces. The second group split the skull into thirds on the axes resulting in 27 pieces. The third and fourth groups split the skull into fourths and fifths respectively, yielding 61 and 95 pieces (Figure 1). These splittings divided the space into 64 and 125 cells, respectively, but some of these cells did not contain bones, and thus the piece count is less than these numbers.

Each splitting group was then linearly compacted to 70% of its original length from 10 different angles. This compaction ratio is within the standard range for overburden stress deformation. The first five deformation angles were confined to the positive X-Y plane. The first angle was 15 degrees oblique to the X-axis, the second 30 degrees, the third 45 degrees, the fourth 60 degrees, and the fifth 70 degrees oblique to the X-axis (Figure 2.1). The last five followed the same spacing configuration as the first but were confined to the positive Z-Y plane (Figure 2.2).

The next step was reconstructing the skull with the deformed pieces. To do this we used two template skulls, the original skull and one deformed template. The deformed template skull is the original Woolly Monkey skull but compacted to 85% of its original width along the previously mentioned X-axis. The skull remained symmetrical but was no longer the true shape. The pieces from each deformation trial were fit onto both template skulls using automated surface recognition and registration techniques.

To measure the relative fit of our reconstructions, we calculated the average distance between the reconstruction and the template. The template and reconstruction were aligned in Rapidform 2004, which then calculated the average distance between the two models by measuring the distance from each vertex of one object to the nearest surface of the other. We used this average distance as the score of fit. To test the symmetry, a mirror image of each skull reconstruction was made and aligned with the original, and then the average distance between the two skulls was calculated by Rapidform 2004 as in the previous case. This average distance was used as the symmetry score. In both cases, the distance found for each vertex was coded in color and plotted on the skull surface as a color distance map to show regional variation in the distance.