Demonstration of the V-shape-constrained HCM. The top row depicts the real data while the bottom shows the synthetic background of Deienno et al. (2021). The red bodies are a priori rejected since they are exterior to the family’s V-shape. The blue bodies are those clustered by the HCM. In the bottom panels, the two bodies are enlarged for clarity and only two bodies are clustered because forming a cluster on the synthetic dataset determines the υ_c (clustering threshold) for the real data. Thus, the blue bodies in the top plot correspond to family members. The black bodies are those who were not a priori rejected but also not clustered at the given υ_c. The plots on the right show the same dataset as the left column but plotted in proper element space, which is the data space to which the HCM is applied.