Triangulation of spatial elementary domains

We consider a domain $\Omega \subset {\mathbf{R}}^3$ that has the form
$$ \Omega=\left\{(x,y,z): a<x<b,\ c<y<d,\ \varphi(x,y)<z<\psi(x,y)\right\}, $$
where $\varphi(x,y)$ and $\psi(x,y)$ are given functions in rectangle $[a,b]\times [c,d]$ which satisfy Lipschitz condition. Let $a=x_0<x_1<x_2<...<x_n=b$ be a partition of the segment $[a,b]$ and $c=y_0<y_1<x_2<...<y_m=d$ be a partition of the segment $[c,d]$. We put
$$ f_{\tau}(x,y)=\tau\psi(x,y)+(1-\tau)\varphi(x,y), \ \tau\in[0,1]. $$
We divide the segment $[0,1]$ by points $0=\tau_0<\tau_1<\tau_2<...<\tau_k=1$ and consider the grid in the domain $\Omega$ defined points
$$ A_{ijl}(x_i,y_j,z_{ijl})=(x_i,y_j,f_{\tau_l}(x_i,y_j)), \ i=0,...,n,\ j=0,...,m,\ l=0,...,k. $$
In this paper we built a triangulation of the region $\Omega$ of nodes $A_ {ijl}$ such that a decrease in the fineness of the partition, and under certain conditions, the dihedral angles are separated from zero to some positive constant.