Surface mapping plays an important role in geometric processing. They induce both area and angular distortions. If the angular distortion is bounded, the mapping is called a {\it quasi-conformal} map. Many surface maps in our physical world are quasi-conformal. The angular distortion of a quasi-conformal map can be represented by Beltrami differentials. According to quasi-conformal Teichm\"uller theory, there is an 1-1 correspondence between the set of Beltrami differentials and the set of...
Source: http://arxiv.org/abs/1005.4648v2