中文摘要：

织物图案中包含着各类蜿蜒曲线、规则与不规则的复杂元素。虽然剪纸图案和分形图案的生成方法已有大量研究工作,但是面向新疆织物图案特点的计算机自动生成方法仍然存在许多挑战性难题。针对新疆织物图案风格化建模难度大的问题,提出图案对称性作为图案生成关键指标,构造循环群和二面体群等变映射与不变映射,研究图案对称性的表征方式,利用对称图案探讨群的映射空间与对称图形之间的关联。通过群映射的仿真实验,绘制混沌吸引子得到群对称图案,有效提高图案的对称性,丰富织物图案的花型设计。

英文摘要：

Fabric design is a kind of complex texture pattern, with winding curve, regular and irregular geometrical patterns as the main pattern. Although the pattern generation methods of paper-cut design and fractal pattern have a lot of research work, the computer automatic generation method for fabric design characteristics in Xinjiang still exists many challenging problems. Considering the difficulties of stylized model building of Xinjiang fabric pattern, the method that uses pattern symmetry as the key index of pattern generation is proposed, build the variable and invariable mapping of cyclic group and dihedral group, study the representation of pattern symmetry, prob the relationship between mapping space of group and symmetric graph using symmetric patterns. Through the simulation experiment of mapping group, the symmetrical design with chaos attractor is drawn. Experiments show the generation method can improve the symmetry of pattern and rich the pattern design of fabric.