  Surface parameterizations have been widely used in computer graphics and
geometry processing. In particular, as simply-connected open surfaces are
conformally equivalent to the unit disk, it is desirable to compute the disk
conformal parameterizations of the surfaces. In this paper, we propose a novel
algorithm for the conformal parameterization of a simply-connected open surface
onto the unit disk, which significantly speeds up the computation, enhances the
conformality and stability, and guarantees the bijectivity. The conformality
distortions at the inner region and on the boundary are corrected by two steps,
with the aid of an iterative scheme using quasi-conformal theories.
Experimental results demonstrate the effectiveness of our proposed method.
