Research On Delaunay Tetrahedralization Of Three-dimensional Degenerate Point Sets

The Delaunay triangulation is one of the most popular and automatic mesh generation methods at present.It can build grids of high quality and change mesh locally.The Delaunay triangulation has wide application in geographical information system,numerical analysis,visualization in scientific computing and medical visualization.It is successful to construct Delaunay triangulations in the two-dimensional space,whereas to construct Delaunay triangulations in the three-dimensional space has many difficulties and needs to be explored in depth.This paper generalized two-dimensional triangulation growth methods to three dimensional space and present a research about three-dimensional Delaunay triangulations.In the construction of the seed tetrahedron,this paper gave a genenral procedure applicable to varieties of circumstances.Aiming at degeneracy in the process of expanding tetrahedron,this paper gave two methods to deal with co-spherical point sets directly,which enhanced the robust of three-dimensional Delaunay triangulation algorithms.Our algorithm is implemented in Intel Visual Fortran development platform.And we do some experiments and use Tecplot software to visualize triangulations.The results show our algorithm is practical.