One important and sometimes contentious challenge in paleobiology is discriminating between species, which is increasingly accomplished by comparing specimen shape. While lengths and proportions are needed to achieve this task, finer geometric information, such as concavity, convexity, and curvature, plays a crucial role in the undertaking. Nonetheless, standard morphometric methodologies such as landmark analysis are not able to capture in a quantitative way these features and other important fine-scale geometric notions.

Here we develop and implement state-of-the-art techniques from the emerging field of computational geometry to tackle this problem with the Mississippian blastoid Pentremites.We adapt a previously known computational framework to produce a measure of dissimilarity between shapes. More precisely, we compute “distances” between pairs of 3D surface scans of specimens by comparing a mix of global and fine-scale geometric measurements. This process uses the 3D scan of a specimen as a whole piece of data incorporating complete geometric information about the shape; as a result, scans used must accurately reflect the geometry of whole, undamaged, undeformed specimens. Using this information we are able to represent these data in clusters and ultimately reproduce and refine results obtained in previous work on species discrimination. Our methodology is landmark free, and therefore faster and less prone to human error than previous landmark-based methodologies.