Warp-Knitted Fabrics Simulation Using Cardinal Spline and Recursive Rotation Frame

To realize 3-D simulation of warp-knitted fabrics, this paper proposes a 3-D loop modeling method based on Cardinal spline and recursive rotation frame method. Fabric structure and loop geometry are studied to form a visible lapping detection model and loop geometrical key points obtained according to chain links and yarn arrangements. In this paper, eight points are set for stitched loop and three points for the inlay. To connect all the control points via a curved line to form a knitted loop shape, the Cardinal spline method is adopted because it is simple to calculate and adjustable in radians. A recursive rotation frame is established to calculate the coordinates of the yarn cross section, eliminating the problem of yarn discontinuity caused by excessive rotation of the moving frame. With the 3-D loop modeling method, some specific mesh and spacer structures are simulated to demonstrate applicability. INTRODUCTION Warp-knitted fabrics, with comparatively complicated structures, are comprised of overlaps and underlaps. Overlaps are looped in the longitudinal direction to form wales while underlaps connect wales in transverse direction. Various overlaps and underlaps are formed when different lapping movements are made by guide needle bars. Yarn coverage is caused as several guide needle bars overlap and underlap at the same time, which additionally adds more complexity challenges warpknitted fabrics designers. With the wide application of computer graphics technology in textiles, computer-aided simulation of warp-knitted fabrics, especially in three-dimensional structures, has become increasingly important. Much research has been done on 3-D simulation of fabrics and yarn modeling, which normally consists of the following two steps: building a yarn path curve according to the fabric structure geometry followed by formation of a 3-D model based on the sectional features of the yarn. There are two popular approaches to building a yarn path curve: in the first, the yarn path curve is directly formed with formulas based on the assumption that the path can be divided into line and arc segments. Baser [1] used a sinus curve, approximating an elastic curve, to draw the yarn curve of woven fabrics. Dabiryan [2] drew warp-knitted loops with straight line segments. Postle [3], Choi [4] and Kurbak [5-6] calculated the geometrical points of weft-knitted loops with trigonometric functions. The other approach is to design key points of yarn path and then form curves using spline interpolation or spline approximation method. Sherburn [7] introduced a method to compute the yarn path with Periodic cubic splines. Yuksel [8] demonstrated the formation of a yarn path for flat-knitted fabrics using cubic CatmullRom interpolation splines. Guo [9] built a yarn path by the Ball B-Splines method. Li [10] created a yarn path for weft-knitted fabrics with NURBS method after getting path control points. Zhang [11-12] and Goktepe [13] applied a similar method to draw warpknitted yarn paths. For the simulation of warp-knitted fabrics, the first approach is appropriate for accurate analysis of loops’ geometry but shows complexity when dealing with various loops. In the cases of approximate splines such as Cubic B-spline and NURBS key geometric points as control points must be calculated separately. Oppositely, interpolative