Conformal energy minimization is an efficient approach to compute conformal parameterization. In this paper, we develop a stable algorithm to compute conformal parameterization of simply connected open surface, termed Stable Discrete Minimization of Conformal Energy (SDMCE). The stability of SDMCE is reflected in the guarantee of one-to-one and on-to property of computed parameterization and the insensitivity on the initial value. On one hand, SDMCE can avoid degeneration and overlap of solution, also, SDMCE is folding free. On the other hand, even if given poor initial value, it can still correct it in very little computational time. The numerical experiments indicate SDMCE is stable and competitive with state-of-the-art algorithms in efficiency.
翻译:非正式能源最小化是计算符合参数化的有效方法。 在本文中,我们开发了一种稳定的算法来计算简单连接的开放表面(称为“稳定分解最小化” ) 的符合参数化。 SDMCE的稳定性体现在对计算参数化的一对一和对一属性的保证和对初始值的不敏感。一方面,SDMCE可以避免溶解的退化和重叠,另一方面,SDMCE正在自由折叠。另一方面,即使初始值很低,它仍然可以在极小的计算时间内纠正它。数字实验表明,SDMCE在效率方面与最先进的算法是稳定和具有竞争力的。