Fig 10. TDA sweeping plane descriptor vectors.

A) The sweeping plane directions are left-to-right (LTR, gray); right-to-left (RTL, orange); bottom-to-top (BTT, cyan); and top-to-bottom (TTB, green). For these four v = iTj filtrations, we started with points on the ith boundary and included more points as we stepped towards the jth boundary. Repeating this process produced the spatial filtration K^v = K₀, K₁…K_end for v = {LTR, RTL, TTB, BTT}. B-D) We formed the Betti curves β₀(K^v) and β₁(K^v) by computing the Betti numbers along each step of K^v for the three blood vessel simulations presented in Fig 7; B) the chemotaxis-driven simulation, C) the haptotaxis-driven simulation and D) chemotaxis and haptotaxis simulation.