| Ruppert's algorithm is an elegant solution to the mesh generation problem for non-acute domains in two dimensions. This thesis develops a three-dimensional Delaunay refinement algorithm which produces a conforming Delaunay tetrahedralization, ensures a bound on the radius-edge ratio of nearby all tetrahedra, generates tetrahedra of a size related to the local feature size and the size of nearby small input angles, and is simple enough to admit an implementation. To do this, Delaunay refinement algorithms for estimating local feature size are constructed. These estimates are then used to determine an appropriately sized protection region around acutely adjacent features of the input. Finally, a simple variant of Ruppert's algorithm can be applied to produce a quality mesh. Additionally, some finite element interpolation results pertaining to Delaunay refinement algorithms in two dimensions are considered. |
