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

IF 17.3 3区 计算机科学 Q1 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Zhengzheng Yin, Yao Jin, Zhijian Fang, Yun Zhang, Huaxiong Zhang, Jiu Zhou, Lili He
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引用次数: 0

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.

Abstract Image

用规则多边形的周期性倾斜对称准规则图案
计算机生成的美学图案作为设计素材被广泛应用于各个领域。最常见的方法是使用分形或动力系统作为基本工具来创建各种图案。为了增强美感和可控性,一些研究人员在使用这些工具的同时还引入了对称布局。一种流行的策略是采用与对称性兼容的动力系统,构建具有所需对称性的函数。不过,这些方法通常仅限于简单的平面对称。另一种则是在倾斜的限制下生成对称图案。虽然这种方法稍微灵活一些,但它仅限于小范围的倾斜,而且缺乏纹理变化。因此,我们提出了一种新方法,利用一般的 k-uniform tilings 对准规则图案进行对称,从而生成美观的图案。我们采用统一的策略来构建 k-uniform tilings 的不变映射,从而消除了 tiling 边缘的纹理接缝。此外,我们还构建了与图案相关的三类对称性:二面对称、旋转对称和反射对称。所提出的方法可以通过 GPU 着色器轻松实现,而且效率很高,适用于带有规则多边形的复杂平铺。实验证明,与最先进的方法相比,我们的方法在灵活控制各种参数的图案生成以及纹理和样式的多样性方面具有优势。
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来源期刊
Computational Visual Media
Computational Visual Media Computer Science-Computer Graphics and Computer-Aided Design
CiteScore
16.90
自引率
5.80%
发文量
243
审稿时长
6 weeks
期刊介绍: Computational Visual Media is a peer-reviewed open access journal. It publishes original high-quality research papers and significant review articles on novel ideas, methods, and systems relevant to visual media. Computational Visual Media publishes articles that focus on, but are not limited to, the following areas: • Editing and composition of visual media • Geometric computing for images and video • Geometry modeling and processing • Machine learning for visual media • Physically based animation • Realistic rendering • Recognition and understanding of visual media • Visual computing for robotics • Visualization and visual analytics Other interdisciplinary research into visual media that combines aspects of computer graphics, computer vision, image and video processing, geometric computing, and machine learning is also within the journal''s scope. This is an open access journal, published quarterly by Tsinghua University Press and Springer. The open access fees (article-processing charges) are fully sponsored by Tsinghua University, China. Authors can publish in the journal without any additional charges.
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