Modelling and Simulation of Weft Knitted Fabric Based on Ball B-Spline Curves and Hooke's Law

With the development of computer techniques and computer graphics, computer aided design (CAD) technology has been applied widely in the textile printing industry. There are many good methods for simulating weft knitted fabric; however, no work on knitted fabric had been performed using ball B-spline curves. In this paper, we have proposed a novel algorithm based on ball B-spline curves and Hooke's Law for modelling weft knitted fabric in 3D. Ball B-spline curves are based on B-spline curves that use data balls instead of data points. By changing the position and the radius of balls of the ball B-spline curves, we can change the thickness and position of the yarn. The loop is the basic unit of knitted fabric; it requires 7 data points to be represented by a ball B-spline curve, and the model is notably fast. At the same time, the model maintains both its accuracy and the geometrical and topological features of the fabric. With VC++ and OpenGL, we added texture and light to simulate different patterns of weft knitted fabric in 3D, including stockinette knit, garter knit, 2-2 rib knit, wing knit, heart knit and stripe knit. Because of the nested structure of knitted fabric, each data point of each loop has changes in a different way when a force is applied to the knitted fabric. The deformation and force on the knitted fabric is modelled using Hooke's Law, which results in a more realistic and faster simulation. We use the parameterization method, and the parameters, such as the radius of ball, the height of a loop, the number of courses, the number of wales and the magnitude of the force, are easy to change. This method is a new means of naturally building and simulating weft knitted fabric in a CAD system.