A Constructive Algorithm for Disk Conformal Parameterizations

Surface parameterization is a fundamental issue widely studied and applied in various image and geometry processing tasks, such as surface registration, remeshing, and texture mapping. In this paper, we propose an efficient constructive algorithm for the computation of disk conformal parameterizations of simply connected open surfaces by combining the spherical harmonic mapping of the doubly covered surface and the geodesic algorithm. In addition, we prove the number of unknowns involved in the computation of the spherical harmonic mapping of the doubly covered surface can be reduced by roughly half. Numerical experiments indicate that the efficiency of the proposed algorithm is improved while the accuracy remains similar or even slightly better compared to the other state-of-the-art algorithms.

Automated summary

In this paper, an efficient algorithm for computing disk conformal parameterizations of simply connected open surfaces is proposed, which combines the spherical harmonic mapping and the geodesic algorithm. The algorithm reduces the number of unknowns involved in the computation and shows improved efficiency compared to other state-of-the-art algorithms, while maintaining similar or even slightly better accuracy.