中文摘要：

为了提高虚拟柔性体力触觉交互中物体形变与力的准确描述及计算效率,提出一种基于球面调和函数表达的柔性体力触觉建模方法。利用球面调和函数的多尺度性进行物体碰撞检测实现,在变形体的密度、杨氏模量、泊松比等参数已知的情况下,根据在力作用下的物体形变使用简化后的波动方程计算变形量和反馈力生成。实验结果表明,采用该方法可以准确描述柔性体的形变过程,其所需的计算成本在可接受的范围之内,可被应用到各种力交互辅助的医学应用中。

英文摘要：

To improve the accuracy of flexible deformation and computational efficiency in haptic rendering,a novel method of soft tissue haptic rendering based on spherical harmonics（SH） representation is proposed.Collision detection is completed with the level of detail of SH.Flexible deformation and force feedback are calculated by simplified deformation wave equation under the condition of changes in the form of density,young modulus and poisson＇s ratio known.Experimental results demonstrate that the computational cost required in computing the updates and the force feedback is significantly less than that encountered in,and accurate flexible deformation is represented.More generally,haptic rendering provides a platform for users to touch virtual objects in simulated environments for the purpose of medical training,virtual diagnosis,treatment planning,surgery and protocol simulation.