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

作　　者：Zhengzheng Yin Yao Jin Zhijian Fang Yun Zhang Huaxiong Zhang Jiu Zhou Lili He 

机构地区：[1]School of Computer Science and Technology,Zhejiang Sci-Tech University,Hangzhou 310018,China [2]Zhejiang Provincial Innovation Center of Advanced Textile Technology,Shaoxing 312000,China [3]School of Media Engineering,Communication University of Zhejiang,Hangzhou 310018,China

出　　处：《Computational Visual Media》2024年第3期559-576,共18页计算可视媒体（英文版）

基　　金：supported by the Key R&D Programs of Zhejiang Province(Nos.2023C01224 and 2022C01220);the National Natural Science Foundation of China(No.61702458);Yun Zhang was partially supported by Zhejiang Province Public Welfare Technology Application Research(No.LGG22F020009);Key Lab of Film and TV Media Technology of Zhejiang Province(No.2020E10015).

摘　　要：Computer-generated aesthetic patterns arewidely used as design materials in various fields. Themost common methods use fractals or dynamicalsystems as basic tools to create various patterns. Toenhance aesthetics and controllability, some researchershave introduced symmetric layouts along with thesetools. One popular strategy employs dynamical systemscompatible with symmetries that construct functionswith the desired symmetries. However, these aretypically confined to simple planar symmetries. Theother generates symmetrical patterns under theconstraints of tilings. Although it is slightly moreflexible, it is restricted to small ranges of tilingsand lacks textural variations. Thus, we proposed anew approach for generating aesthetic patterns bysymmetrizing quasi-regular patterns using general kuniformtilings. We adopted a unified strategy toconstruct invariant mappings for k-uniform tilings thatcan eliminate texture seams across the tiling edges.Furthermore, we constructed three types of symmetriesassociated with the patterns: dihedral, rotational, andreflection symmetries. The proposed method can beeasily implemented using GPU shaders and is highlyefficient and suitable for complicated tiling with regularpolygons. Experiments demonstrated the advantages of our method over state-of-the-art methods in terms offlexibility in controlling the generation of patterns withvarious parameters as well as the diversity of texturesand styles.

关 键 词：quasi-regular patterns(QRP) k-uniform tilings invariant mappings symmetry aesthetic patterns 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]