3维任意域内点集的Delaunay四面体化研究

Delaunay空球准则广泛应用于3维四面体剖分算法,但标准的Delaunay四面体化只适用于点集的凸包区域,且要求不存在多点共球。为了将Delaunay四面体化更广泛地应用于网络剖分,通过引入局部优化三角形面代替Deluany严格的空球准则,提出了3维任意域内点集Deluanay四面体化(DTETAD)的概念,并首先通过若干关键定理的证明,研究了一个四面体划分是DETEAD的充要条件,然后建立了DTETAD的空球准则。该研究成果为拓展Delaunay算法在更广泛范围的应用提供了理论依据。

Delaunay Tetrahedralization in an Arbitrary Domain

The Delaunay criterion of the empty sphere is widely used for 3 dimensional tetrahedron tessellation.But original Delaunay tetrahedralization can not be used for the points set with constrained boundary and the degenerate points set in which four or more points are coplanar or in which five or more points are cospherical.The concept of Delaunay tetrahedralization in an arbitrary domain(DTETAD) is presented based on the definition of local optimized triangulation which is brought out to substitute the strict empty sphere criterion of Delaunay.The sufficient and necessary condition for a tetrahedralization to be a DTETAD are proved,and the conditional empty sphere criterion of DTETAD is presented.The research establishes the theoretic foundation for the application of Delaunay in an arbitrary domain.