# American Institute of Mathematical Sciences

August & September  2019, 12(4&5): 1167-1178. doi: 10.3934/dcdss.2019080

## 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

Received  September 2017 Revised  January 2018 Published  November 2018

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.

Citation: Fang Qin, Ying Jiang, Ping Gu. Three-dimensional computer simulation of twill woven fabric by using polynomial mathematical model. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1167-1178. doi: 10.3934/dcdss.2019080
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##### References:
$\frac{3\ 2}{2\ 3}$ weave diagram
A unit curve and the corresponding coordinate of $\frac{3\ 2}{2\ 3}$ twill weft yarn
A unit curve of twill weft yarn
The segmentation diagram of a unit curve of twill weft yarn
Schematic diagram of a unit of plain fabric weft yarn
Coordinate system of the weft yarn
A unit curve and the corresponding coordinate of the $\frac{3\ 2}{2\ 3}$ twill weave warp yarn
A unit curve of the twill weave warp yarn
The segmentation of a unit curve of the twill weave warp yarn
Segment of the plain warp yarn
The coordinate system of the warp yarn
The curved surface of twill weave weft yarn
The curved surface of twill weave warp yarn
Yarn model and 3D image of $\frac32$ left twill fabric structure
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