Pattern Design And Application Research Based On GeoGebra Curve

With the recent development of computer science and technology and the penetration of digital concepts,more and more patterns are presented in digital form,and pattern design methods have gradually diversified.Mathematics and art are not separated from each other,patterns and digital generation of mathematical graphics have become a new design method.In order to broaden the traditional route of pattern design,enrich the expression method of pattern design and improve the efficiency of pattern design,this topic applies mathematical graphics to pattern design from a mathematical perspective,carries out the factor generation and design transformation of graphics,and applies it to the pattern design of clothing and home textile fabrics,bringing some practical value to the innovative design of patterns.From the mathematical curves,this project uses literature research,experimental methods,comparative analysis and design practice to study the mathematical graphics generated by GeoGebra software,transforming mathematical graphics into design factors,applying design factors to pattern design,and discovering innovative design ideas that combine mathematical graphics with artistic design.Firstly,GeoGebra software is used to generate and intervene in mathematical curves to produce dynamic changes in the curves and to analyze the principles of generation and change in the graphics,mainly using curves generated by mathematical expressions and curves generated in an iterative way as experimental objects,and using comparative analysis to summarise the main features of the curve graphics.Secondly,the curve graphs are transformed into design factors through extraction and reconstruction.The specific segmentation extraction methods are axisymmetric segmentation extraction,unit segmentation extraction and closed curve segmentation extraction;the specific reconstruction methods are derivation by using shape grammar and processing by using the abstract filter method.Through the extraction and reconstruction of design,factors build and optimize the design factor library to be used as a material library for pattern design to complete the transformation of mathematical curves from graphics to design factors.Once again,the physical phenomenon of ice flowers in nature is introduced,the causes and historical implications of ice flowers are analyzed separately,and the patterns are classified through literature,images and other data collection methods,specifically by geometric composition,water vapor abundance and pictorial form,leads to a summary of the artistic characteristics of ice flowers.The design methods are summarised by analyzing market examples of successful applications of ice flower elements.Finally,the design factors are applied to the design of patterns and the simulation of ice flower motifs.In the design of patterns,individual motifs,suitable motifs,and two-sided continuous and four-sided continuous motifs are designed.In the simulation of ice flower motifs,animal,plant,natural and other motifs are simulated.The experiment is intended to demonstrate the feasibility of pattern design using a library of design factors through pattern design and simulation of ice flower motifs.The pattern design is then applied to a series of garment designs,completing the research path from design theory to practical application to demonstrate the innovative and practical value of the constructed design factor library.This research finds that GeoGebra can provide designers with geometric design elements with its relatively simple graphic generation method;the research focuses on introducing mathematical graphics into pattern design and analyzing mathematical graphics from the perspective of the artistic aesthetics of patterns,which can bring innovation in pattern design ideas;the use of the method of extracting and reconstructing design factors to build a design factor library can provide a convenient and efficient method for pattern design Through the experiments of the project and the application practice of patterns,it is proved that the digital way of generating mathematical graphics is feasible in realizing pattern design and pattern simulation,which provides a new idea for pattern design.