Initializing a meta mesh embedding $\Phi(\mathcal{M})$ via Delaunay triangulation creates a very good and robust triangulation, given that the input feature vertices $V_\mathcal{M}$ are well distributed and positioned. Thus, the quality of the triangulation strongly depends on the user input or random seed that determined $V_\mathcal{M}$. In order to further improve this one possibility would be to evenly distribute feature points $V_\mathcal{M}$ before triangulation, perhaps with some user input.
An alternative method is to start with $\Phi(\mathcal{M})=\mathcal{B}$
\put(0.01075236,5.15667685){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}(a) $\mathcal{B}$ with feature \\points $V_\mathcal{M}$ (red)\end{tabular}}}}%
\put(0.01486673,3.39435432){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}(b) Voronoi regions \\of $V_\mathcal{M}$ on $\mathcal{B}$\end{tabular}}}}%
\put(0.01075236,5.15667685){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}(a) $\mathcal{B}$ with feature \\points $V_{\Phi(\mathcal{M})}$ (red)\end{tabular}}}}%
\put(0.01486673,3.39435432){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}(b) Voronoi regions \\of $V_{\Phi(\mathcal{M})}$ on $\mathcal{B}$\end{tabular}}}}%
\put(0.00253664,0.05397902){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}(d) Embedding \\$\Phi(\mathcal{M})$ on $\mathcal{B}$\end{tabular}}}}%