Planar Symmetric Pattern Generation
Ning Lin, Luxi Chen, Huaguan Chen, Jiacheng Cen, Chongxuan Li, Wenbing Huang, Hao Sun
Abstract
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.
Topics
Classified with taxonomy v2 on Wed, 2 Sept 2026.