基于Cosserat理论的头发动态模拟*

针对基于弹性杆理论的超螺旋模型中对动力学方程的求解影响头发模拟实时性的问题，采用Cosserat弹性杆理论对头发建模，引入角速度变量，并加入头发运动平衡的固有约束，得到改进的拉格朗日动力学运动方程;然后，将头发单体离散化，用角速度和四元数作为状态变量简化动力学方程，用半显式的欧拉方程加速方程的执行，大大降低了系统的运行时间，提高了模拟的速度，在满足实时性要求的同时提高了头发模拟的真实度。

Simulation of dynamic hair based on theory of Cosserat

The real-time simulation of hair in the super-helix model based-on the elastic rod is a big problem because of complicatedly solving dynamical equation.Applied Cosserat rod theory to model hair. Obtained the equation of motion by combining the angular velocity with the holonomic constraints in the dynamic equilibrium configuration for an elastic rod. Successfully improved the Lagrangian dynamic equation. Further more,discretized the rod into finite element.Brought the angular velocity together with the quaternions to be the state variables. Decoupled the resulting system of equations. It had gotten an efficient numerical solution of Lagrangian.Used semi-explicit Euler equations to speed up the Lagrangian dynamic equation. Finally, increased the velocity of the simulation,improved the reality of the simulation, satisfied the requirement of fast and realistic simulation of hair.