Abstract:

Objective Due to the complexity and variability of the loop geometry and its arrangement in the fabric, the digital design and simulation of fabrics produced by combining warp-and weft-knitting encounter great challenges. Therefore, it is urgent to establish a scientific and complete mathematical model so as to describe the key information such as pattern, yarn color and loop type of warp-knitted and weft-knitted combined fabrics.

Method As the first step, various matrix models were established, with the values of matrix elements representing different types of loop combinations, yarn colors and warp knitting loop types. According to the geometric characteristics of the warp and weft knitted loops, a three-dimensional model of the loops was established, and the positions of the loops were adjusted according to the pattern matrix information. Consequently, the digital design and simulation of warp and weft knitted fabrics were achieved by using iTDS system.

Results In order to facilitate the precise simulation of warp and weft knitted fabrics, a comprehensive mathematical modeling methodology was innovatively designed. The first step involved the establishment of a matrix representation model of the pattern map, which maps a variety of loop combinations through careful encoding of matrix elements, effectively differentiates different types of warp and weft knitted fabric structures and lays a foundation for the digital representation of complex textures. Furthermore, the color attribute matrix model of warp and weft-knitted yarns was developed, which not only records the color information of a single yarn, but also systematically captures the distribution and change trend of color in the fabric structure, enhancing the visual reality of the simulation results. On top of this, the innovative point of this research was the proposal of a loop type matrix model, which deeply analyzes the different arrangement logic of warp knitted loops on both sides of the fabric, and greatly improves the model's ability to reproduce the complex structure of the actual fabric by precisely defining the spatial configuration rules of each type of loops. Based on the solid framework of the matrix model, a three-dimensional geometric model of the loop was further established, which comprehensively considers the unique geometric features of the warp and weft knitted loops. Through algorithm optimization, the model was enabled to dynamically adjust the coordinate layout of the value points of the loop according to the specific instructions of the pattern matrix, so as to accurately reproduce the micro and macro structural characteristics of the warp and weft knitted fabric in the digital space. Experimental verification results show that the model system constructed in this study not only successfully describes the complex geometric structure of warp-knitted and weft-knitted fabrics, but also achieves a high degree of fidelity in the visual simulation level.

Conclusion This study deepens the understanding of the structure and knitting principle of the warp-knitting and weft-knitting combination, builds a special three-dimensional simulation model, and provides theoretical support and technical guarantee for the industrial production of the warp-knitting and weft-knitting combination. The knitting principle of the combined warp and weft-knitting is elaborated, and the matrix model of yarn color and loop type is constructed. Through the accurate description of the front and back arrangement of the warp knitting loops of different paths, key parameter input is provided for the establishment of the three-dimensional model of the warp-knitted and weft-knitted loops. Based on the geometric characteristics of warp-knitted and weft-knitted knitted loop modes, a three-dimensional model was established, and the position of loop values was adjusted by combining the pattern matrix information, so as to realize the digital design and three-dimensional simulation of warp and weft knitted fabrics. The simulation results show that the proposed mathematical model can effectively describe the combined structure of the fabric, which provides an important theoretical support for the subsequent fabric design and process optimization.

Key words: warp-knitted and weft-knitted combined fabric, knitting process, mathematical model, stitch model, three-dimensional simulation