利用Laplace-Beltrami形状空间的基于样例材料的快速仿真方法

发布时间：2018-05-04 01:27

本文选题：Laplace-Beltrami特征分析 + 基于样例材料　；参考：《计算机辅助设计与图形学学报》2017年09期

【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.
[Abstract]:In physical simulation, when the simulation object and the sample have different topological structure, the existing simulation method based on Laplace-Beltrami operator to construct shape interpolation space on the surface grid will have the loss of accuracy and efficiency in the reconstruction of Euclidean space representation. In order to overcome the above problems, a sample based simulation method based on Laplace-Beltrami shape space is proposed. Firstly, the Laplace-Beltrami operator based on the discretization method of the finite element shape function is proposed to calculate the eigenfunction on the volume grid. After the reconstruction of the eigenfunction, the displacement of the volume mesh is obtained directly, which avoids the approximate projection process. Secondly, the simplified linear interpolation is used to calculate the shape of the target in the shape space formed by the feature function, which improves the efficiency of simulation. Finally, the guiding force of the sample is calculated according to the shape of the target. The shape variant simulation method based on sample material is realized under the finite element simulation framework. The experimental results show that the proposed method can obtain the simulation results similar to the existing methods and has higher simulation efficiency.
【作者单位】：燕山大学信息科学与工程学院;河北省计算机虚拟技术与系统集成重点实验室;北京大学信息科学技术学院;北京市虚拟仿真与可视化工程研究中心;
【基金】：国家自然科学基金(61232014,61421062,61472010) 国家科技支撑项目(2015BAK01B06)
【分类号】：TP391.9

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