一种基于质点弹簧模型的牙龈软组织形变仿真算法

在虚拟手术系统中，软组织形变仿真的好坏会直接影响其仿真的真实感。本文以口腔手术涉及的牙龈软组织为对象，应用质点弹簧模型建立其物理模型，提出一种适用于虚拟手术中牙龈形变仿真的中点平均算法。融合了中点法和平均法的优点，采用中点法对速度进行迭代求解，采用平均法对位移进行求解，能够有效减小误差及受步长的影响。通过与多种欧拉算法对比，进一步验证了中点平均算法求解精度更高、受步长的影响更小的优点。

An Algorithm for Simulation of Gingival Tissue Deformation Based on Mass-Spring Model

In the virtual surgery system, soft tissue deformation simulation will directly affect the reality of the simulation. In this research, a physical model of gingival tissue involved in oral surgery is established by means of mass-spring model. A midpoint-averaging algorithm is proposed for the simulation of gingival deformation in virtual surgery, which combines the advantages of the midpoint method and the average method, and uses the midpoint method to solve the speed and the average method to solve the displacement. It can effectively reduce the error and reduce the impact of step size. Compared with a variety of Explicit Euler algorithms, it is further verified that the midpoint-averaging algorithm has a higher solution precision and is less affected by the step size.