Mesh Optimization

Three criteria for measuring the mesh quality have been defined [CG2Skript, Chapter 2]:

1. Complexity/Efficiency: due to Euler's formula this can be measured exclusively in the number of vertices.
2. Triangle Shape: Triangles can be classified into three categories - Normal triangles where each angle is close to 60 degrees, "needles" or "slivers" with one very small angle and "caps" with two very small angles. The foremost type provides the highest numerical stability when eg. computing normal vectors, while the latter ones behave badly in such situations
3. Triangle Alignment: Describes how well the triangles are aligned to the structure of the mesh. This may have a big impact on the approximation, especially under certain lighting conditions.

There is no single formula for mesh quality, it is always a user-defined combination of the above.