Current geometric optimization methods do not fully consider the overall structure of the model, which may make the effect of geometric optimization of the hex meshes for the models with concave curves unsatisfactory. To this end, this paper proposes an approach to structure-aware geometric optimization of hex meshes. In the approach, by relocating the position of the base complex of the hex mesh, the overall parameterized energy is reduced to obtain an optimized geometric embedding. First, a frame field which conforms to the base complex structure of the input hex mesh is generated. Then, a parameterization that satisfies the structure constraints is established based on the frame field. Finally, the positions of the singular lines of the hex mesh are optimized according to the gradient of the parameterization energy function, and the key isoparametric surfaces are used as the position constraints of the vertices of the patches of the base complex to optimize the whole hex mesh. The experimental results show that the scaled Jacobian value of hex meshes can be effectively improved by the proposed method.

当前的几何优化方法没有充分考虑模型的整体结构，这可能使具有凹曲线的模型的六角形网格的几何优化效果不理想。为此，本文提出了一种六角网格的结构感知几何优化方法。在该方法中，通过重新定位六边形网格的基复合体的位置，可以减少总的参数化能量，以获得优化的几何嵌入。首先，生成符合输入十六进制网格的基本复杂结构的框架字段。然后，基于帧字段建立满足结构约束的参数化。最后，根据参数化能量函数的梯度优化六角形网格的奇异线的位置，关键的等参曲面被用作基础复合体的面的顶点的位置约束，以优化整个六边形网格。实验结果表明，该方法可以有效提高六角形网格的比例雅可比值。