5.2.6 Quality Improvement

Since most quality measures are invariant under rigid transformations, an operation which increases the quality of an element $E \in {\operatorname{AT}}({\Gamma})$ will have no negative effects on elements in other locations. A combined flipping and vertex smoothing approach is often sufficient to obtain a simplex mesh with good quality [32][75]. Both types of operations can safely be performed on the inside of mesh templates as mentioned in Section 5.2.2 and Section 5.2.3. However, for operations on the boundary of a mesh template, there are some restrictions. Flip operations cannot be performed, if at least two elements are in different mesh instances and for vertex smoothing, the search space for the local optimization of quality measures is restricted to the boundary patches. With these restrictions the mesh optimization algorithms can be modified for templated meshes.