做图案生成、剪纸设计或材料拓扑优化的团队，终于有了一个能精确控制任意平面群对称性的数学框架，可以直接用于现有2D生成流程，值得一试。
该论文提出了一种通用的对称化框架，能将任意2D连续表示转换为具有平面群对称性的表示，同时保持连续性。作者给出了数学形式化描述，证明了其对对称函数的逼近能力，并详细说明了构建方法。通过图案设计、剪纸设计、风格化拓扑设计和材料设计四项任务验证了方法的有效性。实验表明该框架能实现有效的对称性控制，具有广泛的应用前景。
Planar Symmetric Pattern Generation
Generating objects with specific symmetries is essential in various real-world scenarios. However, adapting existing 2D continuous representations to enforce planar group symmetry remains a challenge, as the transformation of non-reflective group elements may disrupt continuity. To overcome this limitation, we propose a symmetrization framework for arbitrary planar groups. Our method transforms any 2D continuous representation into a symmetric one while preserving continuity. We provide the mathematical formulation of this representation, demonstrate its approximation capability for symmetric functions, and detail the construction methodology. We validate our approach through three visual design tasks (pattern design, paper-cutting design and stylized topology design) and one material design task. Experiments confirm that our representation enables effective symmetry control and demonstrate its broader applicability.