利用Laplace-Beltrami形状空间的基于样例材料的快速仿真方法  

Efficient Example-based Material Simulation in Laplace-Beltrami Shape Space

作　　者：赵静[1,2] 唐勇 李胜[3,4] 汪国平 Zhao Jing;Tang Yong;Li Sheng;Wang Guoping(College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004;School of Electronics Engineering and Computer Science, Peking University, Beijing 100871;The Key Laboratory for Computer Virtual Technology and System Integration of Hebei Province, Qinhuangdao 066004;Beijing Engineering Research Center for Virtual Simulation and Visualization, Beijing 100871)

机构地区：[1]燕山大学信息科学与工程学院,秦皇岛066004 [2]河北省计算机虚拟技术与系统集成重点实验室,秦皇岛066004 [3]北京大学信息科学技术学院,北京100871 [4]北京市虚拟仿真与可视化工程研究中心,北京100871

出　　处：《计算机辅助设计与图形学学报》2017年第9期1681-1688,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61232014;61421062;61472010);国家科技支撑项目(2015BAK01B06)

摘　　要：物理仿真中当仿真对象与样例具有不同拓扑结构时,现有采用Laplace-Beltrami算子在表面网格上构建形状插值空间的基于样例仿真方法,在重建其欧氏空间表示时会有精度和效率损失.为克服上述问题,提出一种高效地利用Laplace-Beltrami形状空间的基于样例的仿真方法.首先,提出基于有限元形函数离散化方法的Laplace-Beltrami算子在体网格上计算特征函数,该特征函数重建后直接获得体网格位移,避免了近似的投影过程;其次在特征函数构成的形状空间中采用简化的线性插值来计算目标形状,提高了仿真效率;最后依据目标形状计算出的样例引导力,在有限元仿真框架下实现基于样例材料的形变体仿真方法.实验结果表明,该方法可以获得与已有方法相似的仿真结果,并具有更高的仿真效率.The existing example-based simulation method generally utilizes Laplace-Beltrami Operator to construct the shape interpolation space for the surface meshes with different topological structures between the simulated objects and their examples.The loss of precision and efficiency will appear during the reconstruction process in the Euclidean space.To tackle the above issues,we present an efficient example-based material simulation method with the help of Laplace-Beltrami shape space.Firstly,we use linear FEM discretization of the Laplace-Beltrami operator to get the eigen-functions on the volumetric meshes.The reconstruction process obtains displacements of the volumetric meshes directly,which avoids the approximate projection process.Secondly,we utilize the simplified linear interpolation method to compute the target shape in the shape space constructed by the eigen-functions,which can improve the simulation efficiency.Finally,we implement the example-based material simulation on the finite element framework with the example-guided force by the target shape.The experiments demonstrate the benefits of our approach with higher efficiency compared with the similar animation results.

关 键 词：Laplace-Beltrami特征分析 基于样例材料 四面体网格 有限元方法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]