Triangulation of spatial elementary domains

A. A. Klyachin ; A. Yu. Bеlеnikina

Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 4 (2015), pp. 6-12

Résumé

We consider a domain $\Omega \subset {\mathbf{R}}^3$ that has the form $$ \Omega=\left\{(x,y,z): a,\ c,\ \varphi(x,y)\psi(x,y)\right\}, $$ where $\varphi(x,y)$ and $\psi(x,y)$ are given functions in rectangle $[a,b]\times [c,d]$ which satisfy Lipschitz condition. Let $a=x_0$ be a partition of the segment $[a,b]$ and $c=y_0$ 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.

Détail

Mots-clés : triangulation, tetrahedron, partition of domain
Keywords: dihedral angle, elementary domain, Lipschitz condition.