In the previous example, all edges of $\Delta$ were straight lines, but one can perturb them in the sense of Examples 3.9, 3.11 and 3.13. In fact we can form a new $\Delta$ by keeping the vertices fixed and connecting them through smooth curves, which are small perturbations of the straight edges of the previous example. If these curves stay inside the $2$-faces of $B$, then the affine structure on $B-\Delta$ can be defined just like above.