Delaunay Tetrahedralization in an Arbitrary Domain
3维任意域内点集的Delaunay四面体化研究

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.