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# Three-dimensional computer simulation of twill woven fabric by using polynomial mathematical model

• * Corresponding author: Fang Qin
• This study was carried out to obtain visual simulations of twill woven fabrics on a computer screen using certain fabric characteristic. Based on the Peirce model, the polynomial curve fitting method is utilized to simulate the buckling configuration of twill weave yarns. Polynomial mathematical model was never used in constructing twill weave woven fabric structure in the past studies. In polynomial model, each point on yarn buckling track is calculated through the curvature, the radius of the warp and weft yarn, the geometric density, and the buckling curve height. Moreover, the twill weave structure is displayed through the arrangement of the warp and weft yarns. The polynomial mathematical model method was applied to convert the yarn path to a smooth curve and will be provided for three-dimensional computer simulation of satin weave fabric. Different twill weave is displayed by changing fabric parameters. In the VC++6.0 development environment, according to polynomial mathematical model, the three-dimensional simulation of twill fabric structure was given in details through the OpenGL graphics technology.

Mathematics Subject Classification: 68U07.

 Citation: • • Figure 1.  $\frac{3\ 2}{2\ 3}$ weave diagram

Figure 2.  A unit curve and the corresponding coordinate of $\frac{3\ 2}{2\ 3}$ twill weft yarn

Figure 3.  A unit curve of twill weft yarn

Figure 4.  The segmentation diagram of a unit curve of twill weft yarn

Figure 5.  Schematic diagram of a unit of plain fabric weft yarn

Figure 6.  Coordinate system of the weft yarn

Figure 7.  A unit curve and the corresponding coordinate of the $\frac{3\ 2}{2\ 3}$ twill weave warp yarn

Figure 8.  A unit curve of the twill weave warp yarn

Figure 9.  The segmentation of a unit curve of the twill weave warp yarn

Figure 10.  Segment of the plain warp yarn

Figure 11.  The coordinate system of the warp yarn

Figure 12.  The curved surface of twill weave weft yarn

Figure 13.  The curved surface of twill weave warp yarn

Figure 14.  Yarn model and 3D image of $\frac32$ left twill fabric structure

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