In the last years triangle meshes have become increasingly popular and are nowadays intensively used in many different areas of computer graphics and geometry processing. In classical CAGD irregular triangle meshes developed into a valuable alternative to traditional spline surfaces, since their conceptual simplicity allows for more flexible and highly efficient processing. Moreover, the consequent use of triangle meshes as surface representation avoids error-prone conversions, e.g., from CAD surfaces to mesh-based input data of numerical simulations. Besides classical geometric modeling, other major areas frequently employing triangle meshes are computer games and movie production. In this context geometric models are often acquired by 3D scanning techniques and have to undergo post-processing and shape optimization techniques before being actually used in production.