传统几何形纹样是中华优秀传统文化的重要组成部分，对几何形纹样的研究，有助于传统文化在当代的传承和弘扬。论文通过参数化设计理念对传统几何形纹样结构进行衍生和应用研究，旨在能更好的使传统纹样设计与现代数字化设计相结合。

首先，对纹样研究的相关文献进行了可视化分析，简单梳理了传统几何形纹样的形成和发展，归纳分析出纹样结构的相关因素，即文化内涵、工艺技术和审美意识，总结出传统几何形纹样的结构规律和结构特点。然后，对参数化设计的方法和应用进行了论述。最后，经过交叉分析发现：参数化设计有助于解构复杂的几何形纹样，适合研究几何形纹样结构的数理规律，将其引入到计算机图形设计中，有助于提高传统纹样的衍生能力和适用能力。

在实践中，根据传统纹样本身的结构特点，结合复杂性科学中的重构还原理念，确定了进行纹样参数化衍生设计的主要研究思路和一般流程：第一步，拆解目标几何形纹样，确定主要构成元素和构成骨式；第二步，使用规则几何形函数、控制点参数曲线，重构主要元素，以具有位置、方向属性的空间坐标系点集，对应纹样构成骨式；第三步，用坐标系映射的方法重建纹样，生成具有多项可调参数的纹样模型，该模型具有提高传统纹样衍生能力和适用性的特点；最后，在可视化工具Grasshopper中，搭建回形纹、连珠纹等纹样参数模型，进行二维、三维空间中的衍生设计和应用实践，证明了研究思路的可行性。

论文以不改变纹样本身文化内涵为前提，进行几何形纹样结构的参数化构建和衍生设计应用，提出相关设计思路并进行了验证分析。在实例分析和模拟应用中，证明了研究方法有助于提高传统几何形纹样结构的可塑性和适用性，保证了一定的传承性，为传统几何形纹样的现代化发展提供了一种新的思路，具有积极的意义。

Traditional geometric patterns are an important part of Chinese excellent culture. The study of geometric patterns is helpful for the inheritance and promotion of traditional culture in contemporary times. This paper conducts a derivation and application research on the traditional geometric pattern structure through the parametric design concept, aiming to better combine the traditional pattern design with the modern digital design concept.

First of all, used a visual method to analyze the relevant literature on pattern research, briefly combed the formation and development of traditional geometric patterns, summarized and analyzed the relevant factors of the pattern structure, namely cultural connotation, craftsmanship and aesthetic awareness, and summed up the traditional geometric pattern. Structural regularity and structural characteristics of shapes and patterns. Then, the method and application of parametric design are discussed. Finally, after cross-analysis, it is found that parametric design is helpful for deconstructing complex geometric patterns, and is suitable for studying the mathematical laws of geometric pattern structures. Introducing it into computer graphics design is helpful to improve the derivation ability and application of traditional patterns ability.

In practice, according to the structural characteristics of the traditional tattoo itself, combined with the concept of reconstruction and restoration in complexity science, the main research ideas and general process of the parametric derivative design of the pattern are determined: the first step is to disassemble the target geometric pattern, Determine the main constituent elements and form the bone pattern; the second step, use the regular geometric shape function and the control point parameter curve to reconstruct the main elements, and use the space coordinate system point set with the attributes of position and direction to form the bone pattern corresponding to the pattern; third In the next step, the pattern is reconstructed by the method of coordinate system mapping, and a pattern model with a number of adjustable parameters is generated, which has the characteristics of improving the derivation ability and applicability of traditional patterns. The parametric model of the pattern such as pattern is used to carry out derivative design and application practice in two-dimensional and three-dimensional space, which proves the feasibility of the research idea.

On the premise of not changing the cultural connotation of the tattoo itself, the thesis carried out the parametric construction and derivative design application of the geometric pattern structure, put forward the relevant design ideas and carried out verification analysis, and proved the research methods in the case analysis and simulation application. It helps to improve the plasticity and applicability of the traditional geometric pattern structure, and ensures a certain degree of inheritance. It provides a new idea for the modern development of traditional geometric patterns, which has positive significance. completed, and it has been transferred to the actual derivative design. Using this method produces evolution rules that are different from traditional pattern design methods, and improves the plasticity and applicability of traditional geometric patterns.

Based on the premise of not changing the cultural connotation of the tattoo itself, the paper carries out the parametric construction and derivative design application of the geometric pattern structure, and puts forward relevant design ideas and carries out verification and analysis. In the case analysis and simulation application, it is proved that the research method helps to improve the plasticity and applicability of the traditional geometric pattern structure, guarantees a certain inheritance, and provides a new idea for the modern development of traditional geometric patterns. Have a positive meaning.

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