Figure 1.

Examples of automatic mesh quality operations in two-dimensional simulation. Vertices are merged when they are too close (“Vertex merge”) and a vertex splits if the resulting edge is predicted to grow (“Vertex split”, top row). A surface becomes a vertex if its area is too small (“Surface demote”, middle row). Two surfaces collide if a vertex from a surface penetrates the perimeter of a nearby surface (“Vertex insert”, bottom row). Quality operations on bodies convert a body to a vertex when the volume of the body is too small. T1 and T3 transformations are completely reversible by automatic mesh quality operations, whereas $\mathrm{T}2$ transformations can be reversed by replacing a vertex with a surface.