中文摘要：

针对对偶网格萎缩现象,提出一种基于全局能量优化的对偶网格构造方法.该方法从重建原始网格、保持原网格形状和对偶网格质量修正3个角度建立能量优化模型,并通过求解稀疏线性方程组得到对偶网格的顶点位置;得益于该方法的重建能量约束,利用重构约束矩阵与对偶网格顶点位置可以很快地重建原始网格.实验结果表明,文中方法避免了网格萎缩现象,且适用于任何拓扑结构的模型;基于该方法的网格编辑算法可以很好地保持原始网格的几何形状特征.

英文摘要：

To ease the shrinkage problem of dual mesh, a novel dual mesh generating method based on global energy optimization is proposed. The method builds an energy optimization model from three angles： original mesh reconstruction, feature preservation and dual mesh quality optimization. The vertex positions of dual mesh can be obtained by solving a sparse linear system. Benefited from the energy function of reconstruction constraint, original mesh can be reconstructed easily by using reconstruction constraint matrix and the vertex positions of dual mesh. Experimental results show that our method eases the shrinkage problem and can be applied to any mesh with arbitrary topology. A mesh editing algorithm with geometric feature preservation based on the generating method is proposed.