应用三次C-Cardinal样条曲线构建的股线模型

Study on ply yarn model construction by cubic C-Cardinal spline curve

为精确控制股线中心线在三维空间中的弯曲路径,在基于VC++2010和Open GL开源图形库的平台上,采用具有可插值的三次C-Cardinal样条曲线,建立股线中心线三维空间数学模型。采用切面叠加法,即用圆形和非规则多边形作为股线中单纱的切面(横截面),并对其进行适当地平移、旋转,使切面中心点与股线中心线上节点坐标重合,并且使切面垂直于该节点切矢的方向,给股线中心线指定适当数量的节点,并在每个节点处按上述方法添加切面,能够获得光滑无缝连接和加捻无错切的股线表观形态,且股线表观纹理清晰。

In order to precisely control the winding paths of a ply yarn centerline in a three-dimensional space,based on the Visual C＋＋2010 and Open Graphics Library source platform,an interpolatable cubic C-Cardinal spline curve was adopted to establish a ply yarn centerline three-dimensional space mathematical model.The cross section superposition method,i.e.the circular and irregular polygon used as the cross section of yarn in the ply yarn was adopted,appropriate translation and rotation were performed on it to superpose node coordinates on the cross section center point and the ply yarn center point,and to make the cross section perpendicular to the tangent vector of the node,the centerline of the ply yarn is designated with an appropriate number of nodes,and the cross section is added at each node by the method above-mentioned.As a result,the appearance simulation of a ply yarn with the characteristic of smoothness,seamless and non-shear twisting was presented and the ply yarn surface texture was clear.