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Research Article | Open Access

Symmetrization of quasi-regular patterns with periodic tilting of regular polygons

School of Computer Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China
Zhejiang Provincial Innovation Center of Advanced Textile Technology, Shaoxing 312000, China.
School of Media Engineering, Communication University of Zhejiang, Hangzhou 310018, China
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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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Computational Visual Media
Pages 559-576
Cite this article:
Yin Z, Jin Y, Fang Z, et al. Symmetrization of quasi-regular patterns with periodic tilting of regular polygons. Computational Visual Media, 2024, 10(3): 559-576. https://doi.org/10.1007/s41095-023-0359-z

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Received: 28 February 2023
Accepted: 04 June 2023
Published: 27 April 2024
© The Author(s) 2024.

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