虚拟手术中带摩擦的碰撞力计算及其物理仿真研究  

Research of Force Computation and Physical Simulation of Collision with Friction in Virtual Surgery

作　　者：欧惠棠 李晋芳[1] 莫建清[1] Ou Huitang;Li Jinfang;Mo Jianqing(College of Mechanical Engineering, Guangdong University of Technology, Guangzhou 510006, China)

机构地区：[1]广东工业大学机电工程学院,广州510006

出　　处：《中国生物医学工程学报》2018年第3期319-326,共8页Chinese Journal of Biomedical Engineering

基　　金：国家自然科学基金(61300106);广东省科技计划项目(2016A040403108)

摘　　要：虚拟手术训练中,碰撞力的计算必不可少,常见的碰撞力计算中,经常会忽略碰撞体之间的摩擦。提出一种带有摩擦的碰撞力计算方法。首先,建立计算机图形学物理仿真中最为常用的粒子系统,总体的常微分方程通过隐式欧拉方法求解,通过碰撞检测找出潜在的碰撞点,建立碰撞约束和摩擦约束数学模型,再通过类高斯-赛德尔算法求解出摩擦接触力。然后分别进行10次单接触面和双接触面的接触碰撞实验,分析其相应时间和稳定后起伏平均值,再进行100次多接触点碰撞实验,分析其平均运算时间。实验表明,在单接触面和双接触面接触的情况下,模型碰撞的平均响应时间为0.02 s,接触力稳定后的平均起伏范围为±0.02个单位。在多接触点接触的实验中,11个接触点接触时,平均每个接触点的运算时间为1.9 ms,满足物理仿真的实时性要求。In the virtual surgery training,the computation of collision force is indispensable. Usually,the friction between colliders is neglected in the computing contact force. This paper proposed a method to compute the contact force with friction. First,the particle system that is widely used in physical simulation in computer graphics was established. And the total ODEs were solved through implicit Euler method. Then,the potential contact points were found out through collision detection and the mathematical models of collision constraints and friction constraints were constructed,and subsequently the contact force with friction was computed by Guass-Seidel-like algorithm. Then 10 single contact and double contact surface contact collision experiments were carried out respectively,and then 100 multiple contact surface collision experiments were carried out,and the average operation time was analyzed. The experimental results showed that the average response time of the model collision was 0. 02 s under the contact of single contact surface and double contact surface,and the average fluctuation range was in the range of ＋ 0. 02 units after the contact force was stable. In the experiment of the contact of multi contact surface,the average operation time of each contact point was 1. 9 ms when 11 contact points contact,which could meet the real time requirement of physical simulation.

关 键 词：虚拟手术 粒子系统 带摩擦的碰撞仿真 隐式欧拉方法 高斯-赛德尔算法 

分 类 号：R318[医药卫生—生物医学工程]