质点弹簧模型在牙龈软组织形变仿真上的改进与应用  

Improvement and Application of Mass Spring Model in Simulation of Gingival Soft Tissue Deformation

作　　者：马天[1] 李娇娇 李占利[1] 李远成[1] Ma Tian;Li Jiaojiao;Li Zhanli;Li Yuancheng(School of Computer Science and Technology,Xi’an University of Science and Technology,Xi’an 710054)

机构地区：[1]西安科技大学计算机科学与技术学院

出　　处：《计算机辅助设计与图形学学报》2020年第2期325-333,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金重点项目(61834005);中国博士后科学基金(2016M602941XB)

摘　　要：牙龈软组织的形变仿真和建模是虚拟牙齿矫正系统的重要部分.针对外力过大时传统质点弹簧模型引起的牙龈脱落牙齿的"超弹性"问题,在传统"面模型"的基础上,通过对比形变效果和形变速度来设置形变弹簧最优阈值.当形变弹簧缩短或伸长超过阈值时,将弹簧长度恢复为原始长度以作为下一次单步形变的初始长度,从而使面模型具有一种"体"的特征.在形变结束后采用"光滑度之和"来度量牙龈表面的光滑度,该方法从数值上对光滑度进行合理定义.在VTK环境下实现改进模型及相关模型,在真实扫描的牙颌三维模型数据上进行牙龈软组织形变仿真对比实验.结果表明,改进模型形变速度提高28%以上且光滑度之和明显降低,说明改进模型在保证较快形变速度的前提下较好地解决了超弹性问题.It is an important part of virtual orthodontic system that simulates and models the gingival soft tissue deformation.Aiming at the problem of"hyper-elasticity"of gingival exfoliated teeth caused by the traditional mass spring model when the external force was too large,the optimal threshold of the deformation spring was set by comparing the deformation effect and the deformation speed on the basis of the traditional"surface model".When the deformation spring was shortened or elongated beyond the threshold value,the spring length was restored to the original length as the initial length of the next single step deformation,so that the"surface model"has a"body"feature.The"sum of smoothness"was used to measure the smoothness of gingival surface after deformation,which gave a reasonable numerical definition of smoothness.The improved model and related models were implemented in VTK environment.The contrast simulation experiments of gingival soft tissue deformation were carried out on real scanned three-dimensional model data of jaw.The results show that the deformation speed of the improved model is increased by more than 28%and the sum of smoothness is obviously reduced.So,the improved model can solve the problem of hyper-elasticity well on the premise of higher deformation speed.

关 键 词：质点弹簧模型 软组织变形 超弹性 牙齿矫正 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]