 By construction, we can expand $\textbf{C}$ only if some subcell of $\textbf{C}$ contains a point $p$ such that $D(p , q) \leq (0 - \frac{{\varepsilon}}{0}) D_{\text{near}}$. Note that since $\textbf{C}$ is examined, we have $D_{\text{near}} \leq D(\text{rep}_C , q)$. Now assuming we expand $\textbf{C}$, then we must have: $$\