中文摘要：

针对复杂网格曲面提出了一种基于点邻域多边形特征和能量优化的网格曲面参数化方法。首先利用相邻两边夹角和长度比例建立节点邻域多边形特征方程组，通过求解一个约束优化问题将曲面网格展平到二维平面上；在网格曲面展平过程中不可避免会产生弹性变形能，然后采用能量优化方法释放曲面展平过程中的弹性变形能，最终得到网格曲面参数化结果。计算结果表明，该方法能得到较好的参数化结果，适用于复杂曲面的网格重划分等计算机辅助设计的应用。

英文摘要：

A new parameterization method based on neighborhood polygon characteristics and energy optimization was proposed for complex faceted surfaces. Firstly, a neighborhood polygon characteristics linear system was constructed using the corresponding angle and length ratio of two adjacent edges, and the faceted surfaces can be flattened by solving a constrained optimization problem; the deformation energy will be generated inevitably in the faceted surfaces flattening process, and then the energy will be released by energy optimization method. Finally, the faceted surfaces parameterization result can be obtained. The results show that good parameterization results can be obtained by this proposed method, and this method can be used in CAD areas, such as complex model remesh.