Abstract
Computer-generated aesthetic patterns are widely used as design materials in various fields. The most common methods use fractals or dynamical systems as basic tools to create various patterns. To enhance aesthetics and controllability, some researchers have introduced symmetric layouts along with these tools. One popular strategy employs dynamical systems compatible with symmetries that construct functions with the desired symmetries. However, these are typically confined to simple planar symmetries. The other generates symmetrical patterns under the constraints of tilings. Although it is slightly more flexible, it is restricted to small ranges of tilings and lacks textural variations. Thus, we proposed a new approach for generating aesthetic patterns by symmetrizing quasi-regular patterns using general k-uniform tilings. We adopted a unified strategy to construct invariant mappings for k-uniform tilings that can eliminate texture seams across the tiling edges. Furthermore, we constructed three types of symmetries associated with the patterns: dihedral, rotational, and reflection symmetries. The proposed method can be easily implemented using GPU shaders and is highly efficient and suitable for complicated tiling with regular polygons. Experiments demonstrated the advantages of our method over state-of-the-art methods in terms of flexibility in controlling the generation of patterns with various parameters as well as the diversity of textures and styles.
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Acknowledgements
This work was supported by the Key R&D Programs of Zhejiang Province (Nos. 2023C01224 and 2022C01220) and the National Natural Science Foundation of China (No. 61702458). Yun Zhang was partially supported by Zhejiang Province Public Welfare Technology Application Research (No. LGG22F020009), and Key Lab of Film and TV Media Technology of Zhejiang Province (No. 2020E10015).
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Zhengzheng Yin is a master student at the School of Computer Science and Technology, Zhejiang Sci-Tech University, China. His research interests include computer graphics and generation of digital art graphics.
Yao Jin is an associate professor at the School of Computer Science and Technology, Zhejiang Sci-Tech University, China. His research interests include computer graphics, digital geometry processing, and digital art graphics.
Zhijian Fang is a lecturer at the School of Computer Science and Technology, Zhejiang Sci-Tech University. His research interests include big data and AI algorithms.
Yun Zhang is currently a professor at Communication University of Zhejiang. His research interests include computer graphics, image and video editing, and computer vision. He is a member of CCF.
Huaxiong Zhang is a professor at the School of Computer Science and Technology, Zhejiang Sci-Tech University. His research interests include intelligent information processing and generation of digital art graphics.
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Yin, Z., Jin, Y., Fang, Z. et al. Symmetrization of quasi-regular patterns with periodic tilting of regular polygons. Comp. Visual Media 10, 559–576 (2024). https://doi.org/10.1007/s41095-023-0359-z
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DOI: https://doi.org/10.1007/s41095-023-0359-z