Wang Charlie
Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, PR China.
IEEE Trans Vis Comput Graph. 2008 Jan-Feb;14(1):25-36. doi: 10.1109/TVCG.2007.1067.
Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.
各种应用都要求无拉伸的表面扁平化。目前，最困难的问题是如何将给定模型分割成近似可展的地图集，以便能够计算出近似无拉伸的扁平化。需要分割标准来评估扁平化给定曲面片的可能性，并且该标准应能快速计算。在本文中，我们提出了一种计算网格面片的长度保持自由边界（LPFB）的方法，该方法加快了网格参数化的速度。然后，参数化中的变形可作为一种试错算法的标准，用于将给定模型分割成近似可展的地图集。LPFB的计算被表述为角度空间中的一个数值优化问题，在该问题中，我们试图在保持由闭路定理和长度保持导出的约束的同时，优化边界上的角度盈余。
