Mesh generation with quasi-equilateral triangulation.
Joon Young Park · Deep Blue (University of Michigan) · 1991
A new algorithm for generating two-dimensional uniform and graded finite element meshes is developed and implemented. The algorithm requires an initial triangulation of the given object. Using several operators developed in this dissertation, nodes are generated on the boundary as well as on the interior of the object. These nodes are then used to generate a triangular mesh with the desired density. Most importantly, the algorithm guarantees a lower bound of 30$\sp\circ$ on the smallest angle in the whole mesh. With this guaranteed lower bound, smoothing of the initial mesh or human interventions to improve the shape of the mesh become unnecessary. In three dimensional space, a new criterion--the solid angle--is introduced to measure the quality of tetrahedral meshes. The properties of solid angles and analogies from two dimensional meshing algorithms have been studied and are proposed for utilization in three dimensional meshing algorithms. Also, difficulties encountered in developing three dimensional meshing algorithm are discussed.