In the picture below, I'm having some difficulty in understanding the 2nd condition.
Why does the second condition make $\Gamma$ lie on one side of its relative boundary?
If $\Phi_p$ flattens $\partial \Omega$ near $p \in \partial \Omega$ onto a subset of $\{z_n=0\}$, then $\Psi_p$ flattens $\partial \Gamma$ onto a subset of $\{z_n=0, z_i=0\}$, where choosing the $i$-th coordinate will determine the $\Psi_p$ function?
