Fabric modeling based on Riemann zero curvature

Fabric has complicated anisotropic mechanical behavior because of the woven pattern and complex physical properties. However, most current fabric simulation models are not satisfied because the models are usually geometrical models with stiffness parameters.

In this paper, the authors present a modeling technique to simulate fabric with Riemann manifold. The proposed nonlinear model is formed with ridge wave-curved surface based on the Riemann zero curvature, and the authors develop a solution to conserve the surface area. It decomposes the m × n matrix constituting the fabric into several batches and processes the fabric dots in batches. In this model, the distance between any two adjacent particles of the fabric's is assumed to be equal, and the area of the curved surface is always constant, and the inclination and decay of the ridge wave-curved surface are also considered.

As the result, the simulated shape is lifelike. In time cost performance, the model improves the efficiency of the fabric styling and meets the requirements of real-time simulation.

The proposed nonlinear model is formed with ridge wave-curved surface based on the Riemann zero curvature, and the authors develop a solution to conserve the surface area.