闭合三角网格的优化切割与保角映射

提出一种自动地将任意闭合三角网格切开并保角映射到二维平面域的算法.通过对自动提取的模型初始切割线逐步优化得到模型切割线,优化过程由一个与保角映射扭曲度和合法性相关的成本函数控制.为了减小映射扭曲,算法中不预先固定参数域边界,而在参数化过程中自动地确定网格的自然边界.实验结果表明,该算法通过优化切割线和参数域边界有效地降低了三角形形状扭曲,并保证了参数化结果的合法性.

Optimized Cutting and Conformal Mapping for Closed Triangular Meshes

We propose a method to cut and map a closed triangular mesh onto a 2D planar domain automatically. The initial cut is optimized iteratively controlled by a cost function related to the distortion and validity of conformal mapping of the mesh. During parametrization, Rather than fixing the boundary of the parametric domain a priori as most current methods did, we allow the boundary to be generated naturally. Experimental results show that our algorithm reduces the geometric distortion effectively and ensures the validity of the conformal mapping.