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

Fang Qin; Ying Jiang; Ping Gu

doi:10.3934/dcdss.2019080

Article Contents

2019, Volume 12, Issue 4&5: 1167-1178. Doi: 10.3934/dcdss.2019080 open access

This issue Previous Article The heterogeneous fleet location routing problem with simultaneous pickup and delivery and overloads Next Article Vulnerability of super connected split graphs and bisplit graphs

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

1.
Art School, Jinling Institute of Technology, Nanjing 211169, China
2.
School of Fashion Art and Engineering, Beijing Institute of Fashion Technology, Beijing 100029, China
3.
College of Textile and Clothing Engineering, Soochow University, Soochow, 215021, China
4.
National Engineering Laboratory for Modern Silk, (NELMS) Soochow, 215123, China

* Corresponding author: Fang Qin
* Corresponding author: Fang Qin

Received: August 31, 2017

Revised: December 31, 2017

Published: March 2019

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Abstract

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.

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Mathematics Subject Classification: 68U07.

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

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

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Figure 3. A unit curve of twill weft yarn

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

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

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Figure 6. Coordinate system of the weft yarn

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

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

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

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Figure 10. Segment of the plain warp yarn

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Figure 11. The coordinate system of the warp yarn

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Figure 12. The curved surface of twill weave weft yarn

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Figure 13. The curved surface of twill weave warp yarn

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

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