基于质点刚性杆模型的织物三维模拟

Cloth 3-D simulation based on the mass-rod model

分析质点弹簧模型的基本原理、方法及其特性,将织物离散化成呈正方形分布的质点网格,把质点的弹簧连接变成刚性杆相连,并将作用在质点上的外力通过刚性杆直接传递到相邻质点上,构建了质点刚性杆模型。根据牛顿基本物理学定律,建立织物的力学方程,采用Verlet积分法对质点空间位移进行计算,利用Jacobi松弛算法保证质点间刚性杆的约束特性,实现对织物三维状态的模拟。同时,设置了空间物体,实现了织物对外界物体碰撞的简单处理,验证了模型对多约束叠加的适应性。该模型简单实用,其算法收敛稳定,并获得良好的实时效果。

The basic principle, method and characteristics of the mass-spring model are analyzed. The cloth is digitized as the mass grid with square distribution, the spring connections acting upon mass are replaced by the connections of rigid rod, the external forces acting upon mass are transmitted to the adjacent mass directly through the rigid rod, and the mass-rod model is constructed. According to Newton basic physical law, the mechanical equation of cloth is derived. The 3-D location of the mass is calculated using Verlet integration, the characteristic of rigid-rod restriction comes true using Jacobi relaxation, and cloth 3-D simulation is completed. In the meantime, the collision object is set, the handling of cloth in collision with outside object is accomplished. The adaptability of the model＇s multiple constraints is verified. The model is simple and practical, its algorithm is stable and convergent. The excellent real time effect is obtained.