Fast Disk Conformal Parameterization of Simply-connected Open Surfaces
This work addresses a domain-specific problem in computer graphics and geometry processing for researchers and practitioners needing efficient surface parameterizations.
The paper tackled the problem of computing disk conformal parameterizations for simply-connected open surfaces, resulting in a novel algorithm that significantly speeds up computation, enhances conformality and stability, and guarantees bijectivity.
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.