研究平面图案对称性，发现人眼感知与数学理论不符
Challenges in Plane Symmetry: From Theory to Perception
- 用群论分析四种基本几何操作生成的对称模式
- 实验显示人类感知的对称性与理论预测不一致
- 揭示认知与数学对称之间的差异，适合认知科学读者
平面装饰图案通过平移、旋转、反射和滑动反射四种基本几何操作重复基础单元生成。根据群论，这些操作的不同组合对应不同的对称群。本文选取一个具有挑战性的装饰图案，从理论和感知两个角度进行分析。实验结果表明，参与者所感知到的对称性与理论预测存在明显偏差。
原文摘要 · Abstract (English)
The planar ornaments are created by repeating a base unit using a combination of four primitive geometric operations: translation, rotation, reflection, and glide reflection. According to group theory, different combinations of these four geometric operations lead to different symmetry groups. In this work, we select a single challenging ornament, and analyze it both from the theoretical point of view and perceptual point of view. We present the perceptual experiment results, where one can see that the symmetries that the participants perceived from the ornaments do not match to what the theory dictates.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。