Block-balanced meshes in iterative uniform refinement

In this paper we study and delimit a property of known four triangle subdivisions that is useful in tri to quad mesh conversion methods. We provide both theoretical results and empirical evidence showing that iterative application of the four triangles longest-edge subdivision and the four triangles similar subdivision produces block-balanced meshes, meshes in which triangle pairs sharing a common longest edge tend to cover the area of the entire mesh. Some other properties of such triangle subdivisions regarding mesh quality and adjacency relationships are also discussed.