An Efficient Energy Minimization for Conformal Parameterizations

作者：Yueh Mei Heng^*; Lin Wen Wei; Wu Chin Tien; Yau Shing Tung

来源：Journal of Scientific Computing, 2017, 73(1): 203-227.

DOI：10.1007/s10915-017-0414-y

• Conformal energy minimization
• Conformal parameterizations
• Simply-connected open surfaces
• Surface morphing

Surface parameterizations have been widely applied to digital geometry processing. In this paper, we propose an efficient conformal energy minimization (CEM) algorithm for computing conformal parameterizations of simply-connected open surfaces with a very small angular distortion and a highly improved computational efficiency. In addition, we generalize the proposed CEM algorithm to computing conformal parameterizations of multiply-connected surfaces. Furthermore, we prove the existence of a nontrivial accumulation point of the proposed CEM algorithm under some mild conditions. Several numerical results show the efficiency and robustness of the CEM algorithm comparing to the existing state-of-the-art algorithms. An application of the CEM on the surface morphing between simply-connected open surfaces is demonstrated thereafter. Thanks to the CEM algorithm, the whole computations for the surface morphing can be performed efficiently and robustly.

• 出版日期2017-10