织物结构的多项式数学模型与三维模拟

Polynomial Model and 3d-simulation of Fabric Structure

在Peirce模型的基础上,利用多项式曲线拟合的方法模拟纱线的屈曲形态,以纱线弯曲的曲率、经纬纱线的半径、几何密度、屈曲波高来计算纱线屈曲轨迹上的每个点,再通过经纬纱线的排列来展示织物的结构图。在VC++6.0开发环境下,按照多项式数学模型,利用OpenGL图形技术实现了平纹和斜纹织物结构的三维模拟。模拟时,能对图形进行移动、旋转、缩放等图形定位操作;能改变一个或几个结构参数,展现经、纬纱在织物中的屈曲交织形态,并瞬时显示改变后的三维图形;通过改变法线向量的求法,改变织物结构模拟的光照效果。

This paper employs the polynomial curve fitting to simulate the flexing state of yarns instead of the bowing modality of using straight lines and curves in Peirce model. The method adopted in this paper, which chooses polynomial curve fitting that combines the bowing curvature of yarns, radius of warp and weft, thread-spacing, crimp amplitude to calculate every spot in flexing trace of yarns as well as defining structure through the arrangement of warp and weft, better describes the actual structure of fabric.Through the established mathematical model combined with advanced OpenGL graphical function base, VC＋＋6.0 developing environment and the illumination model inside OpenGL ascribed to it, this research realizes the 3D simulation of plain weave and twill weave. The established model has graphic defining operations such as translation, rotation, scale etc. and it is able to change illumination effect in some degree as well as instantly manifesting the diverse 3D graphs according to the varying parameters.