Research On Efficient Cloth Simulation Based On Mass-Spring Model

In the past decades, cloth simulation has become more and more important in research areas of computer graphics. Due to rapid development of computer technology, today's cloth simulation can simulate cloth deformation through computer animation. But the technology still can not meet the demands of our information age. With the rapid development of the Internet, e-commerce, on-line shopping and on-line games have put great demands on realistic and real time cloth simulation. Thus there is still a lot of research work to be done in this area. Fast and realistic cloth simulation still remains a challenge.In the early stage of cloth modeling, geometry approaches are usually employed, but the results are poor. Since the employment of physically based approaches,cloth animation has gained great progress. However, these methods are usually not very efficient or the physical plausibility is poor. The main problem is that physically based approaches involve numerically solving a differential equation, and the numerical instability limits the time step. Thus, the computation cost is very expensive.The goal of this thesis is to develop a stable cloth simulation method that can also meet real time requirement. To achieve this goal, the physical and mechanical properties of real cloth were analyzed and several cloth simulation methods were compared. Method based on mass-spring model was chosen. Dynamics equations of cloth simulation were established based on Newtonian mechanics. These equations were solved using Verlet integration method for its fast computation speed and can develop a stable animation. Another important part of cloth simulation is how to deal with collision between the cloth and other rigid objects. To achieve real time effect, a simple and efficient collision detection method based on distancefield method was developed to deal with collisions with specific rigid object.The author first proposes a mass-spring model developed for rectangle meshes based on the survey of cloth modeling methods, by which the simulation of cloth is formulated unified. The dynamic system of modeling and simulation is derived and solved using time differentiates method, with given composition and expression of internal and external cloth forces in the formulation. To overcome the serious weakness representing cloth properties simply of previous model, the improved mass-spring model considers mechanical properties of cloth such as stretching, shearing and bending with different stiffness of spring, which can improve the realistic effect.Verlet integration has the benefit of being quite stable; especially in the face of enforced boundary conditions (there is no explicit velocity term with which the position term can get out of sync). It is also very fast to compute (almost as fast as Euler integration), and under the right conditions it is 4th order accurate (by comparison, the Euler method is only 1st order accurate, and the second order Runge-Kutta method is only 2nd order accurate. The disadvantages of the Verlet method are that it handles changing time steps badly, it is not a self-starter (it requires 2 steps to get going, so initial conditions are crucial).This thesis then gives the general framework and some typical method of collision problem. With the need for fast cloth simulation, the author proposes an efficient solution to the collision problem, where the surfaces are triangulated. The idea is to develop a distance field with is based on a 3-SEDT method. We first describe the method for calculating the distance field. Only the rigid objects of an environment are represented by distance fields, then with the signed distance field, we may also determine if thepoint is internal or external to objects within the domain.Then, we propose a method for rapid collision response between rigid bodies and deformable objects like cloth. We decided to solve this problem approximately by not testing each triangle of the deformable object, but considering only the vertices. Clearly, we now have to hold those vertices about a predefinedεaway from the surface to avoid artifacts. Collisions are resolved simply by moving particles back to the surface of the object. Notice, that in our system possible collisions are not affecting the computation of forces of the particle system. Although techniques for incorporating collision information exist, we have chosen not to use them because of the increased time complexity.Due to the fact that the springs are"ideal"and they have unlimited linear deformation rate. The major drawback of the mass-spring cloth model is its"super elasticity". We cope with the super-elasticity using position modification proposed by Provot. This method is mostly fit our Verlet integration schedule and the collision response.The simulation program was developed using Microsoft Visual C++6.0. OpenGL was used for 3D scene rendering and animation; the program can simulate the entire process of cloth descending and colliding with spheres. Real time realistic cloth deformation and collision response was achieved. In conclusion, the results of our research results enrich the approaches to cloth simulation technology. We hope that intensive and further research will be aroused through our research, and facilitate the development of relative technology in future.