基于函数拟合的中国传统服饰纹样数字化复原方法研究OA

Traditional patterns not only carry profound historical contexts but also disseminate excellent culture and spirit.To effectively promote the dissemination of traditional patterns,this study focuses on fabric patterns from ancient Chinese paintings and employs mathematical function fitting technology to achieve precise restoration of these patterns. Eight representative geometric,animal,plant,and natural/artifact patterns were selected.These patterns were extracted from clear,flat sections of classical paintings and vectorized.By using mathematical tools such as GeoGebra and Desmos,the patterns were fitted and optimized through mathematical functions and equation systems.Specifically,the workflow involved:segmenting and classifying local features of the patterns;extracting key characteristic points and curves using mathematical tools;fitting the pattern contours via function expressions while adjusting parameters to optimize geometric consistency;and defining variable ranges and combining partial functions to construct complete digital pattern designs. Subjective evaluations from 60 design students demonstrated that the generated digital patterns not only accurately restored the morphological characteristics of traditional motifs but also exhibited adjustable and easily applicable mathematical properties.This study innovatively integrates mathematical function tools with traditional visual artistic expression,opening new interdisciplinary pathways for transforming traditional art into digital visual art. The results also revealed that the digital method significantly enhances the visual reproduction and practical application value of patterns.However,for highly complex patterns,further optimization of fitting algorithms and workflow efficiency is required.Additionally,the tool-dependent nature of the method highlights the need for technical accessibility.These limitations guide future research directions,emphasizing the enhancement of technical compatibility while preserving cultural uniqueness,thereby expanding possibilities for the digital exploration of traditional culture. By translating fabric patterns from classical Chinese paintings into mathematical expressions,this study establishes an interdisciplinary approach that combines artistry and scientific rigor.The classification and vectorization of patterns laid the foundation for precise extraction,while the use of GeoGebra and Desmos for mathematical function fitting overcame the limitations of traditional graphical representation,improving pattern accuracy and reproducibility. Furthermore,the research holds profound socio-cultural implications.Mathematical expressions allow patterns to exist in standardized forms,preserving their visual morphology while revealing their intrinsic structures and cultural meanings.This method enhances preservation efficiency and broadens application fields,particularly in international collaboration.The universal mathematical language facilitates cross-cultural artistic exchange,offering possibilities for cultural innovation and integration in a globalized context.