Generate Good Mesh Eeciently

We consider the following meshing problem. Given a control spacing function f(), which speciies the desired element size, how to generate a well-shaped and a well-conformed mesh. Here, well-shaped mesh means that the circumradius-to-shortest-edge-length ratio of the mesh is bounded from above by a constant; well-conformed means that the element size is within a constant factor of f(). Li et. al. recently proposed a new method named biting, which combines the strengths of advancing front and circle packing and generates high quality mesh. In this paper, we show that biting squares instead of circles not only generates high quality mesh but also is very ef-cient in the sense that the time complexity of the algorithm is O(n log n) in 2D, where n is the number of mesh vertices generated. And it can be easily extended to 3D.