Dynamic Simulation Of Fabric Based On Riemann Manifold

With the development of 5G and VR/AR technology,people are constantly pursuing accurate model generation and realistic animation experience.As a typical representative of flexible materials,fabric modeling and simulation has always been a hot spot and difficult point in computer graphics and related fields,and is widely used in computer graphics and vision,film and television animation,virtual reality,animation games and other fields.In recent years,many scholars on the basis of predecessors' work,continuous improvement,and explore new fabric simulation technology,but more research is in the European space exploration and improvement of fabric simulation model,although after the continuous efforts of the experts and scholars,but still exists the existing fabric simulation modeling complex,poor stability,such as slow convergence speed and the simulation effect is not distinct.In this paper,a manifold theory based on Riemann space is proposed to study the dynamic simulation of fabrics.By understanding the basic knowledge of manifolds,measurements and curvature in Riemann space,the Riemann metric tensor and Riemann curvature tensor in Riemann geometry are applied to the research work in this paper,which provides theoretical support for the establishment of a fabric simulation model based on Riemann manifolds.The physical properties of the fabric are analyzed and the physical parameters of the fabric are extracted by principal component analysis.A fabric simulation model based on Riemann manifold is established by considering the internal energy generated during the deformation of the fabric surface and the action of various forces generated by the external environment during the simulation of the fabric.Considering the discrete element is small enough in Riemannian space can also be seen as the European space curved surface,so this article in the simulation model is set up,the first fabric surface discrete into quadrilateral finite element grid,then using Riemannian metric tensor and Riemannian curvature tensor calculation surface deformation was produced by the internal deformation energy,and further to analyze of the forced state of a fabric,fabric dynamic simulation of differential equation,using the finite element method to solve differential equations.Finally,the algorithm is verified by experiments.The experimental results show that the proposed fabric simulation model is simple,flexible and fully considers the physical properties of the fabric.At the same time,thesolution method of the dynamic simulation equation guarantees the real-time performance of the simulation,and the visual effect is realistic,which is close to the appearance deformation of the real fabric under the same external conditions.