随机聚类形状匹配的形变体实时仿真
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摘要
针对传统形状匹配方法仅限于模拟较小形变的问题,提出一种基于随机聚类的划分方法.首先对传统旋转矩阵的求解过程进行优化,引入位置约束因子对目标位置进行二次修正,避免穿透现象;然后利用随机聚类方法对粒子群集进行划分生成一系列相互重叠的聚类,在单个时间步长内对每个聚类进行刚度拟合变换,重叠区域的粒子属于多个聚类,在形变过程中进行多次旋转变化能够模拟更大尺度的形变效果;最后采用反距离平方内核的权重方案计算重叠区域粒子的质量,根据粒子与所属簇集的距离合理地分配质量比重更新聚类中心.文中方法在每一次聚类更新时及时更新权重和质心,有效地避免了粒子在划分过程中产生较大偏移.实验结果表明,该方法能快速划分任意模型的粒子群集,允许模拟大尺度弹性形变,与形状匹配相结合具有较强的鲁棒性;同时保证了其实时性,更加适用于交互仿真.
Aiming at the problem that the traditional shape matching method is limited to small deformation simulation, a partitioning method based on random clustering was proposed. Firstly, the solution of the traditional rotation matrix was optimized. And the position constraint factor was introduced to re-correct the target position to avoid the penetration phenomenon. Secondly, a random clustering strategy was used to divide the particle clusters to generate a series of overlapping clusters. Each cluster was dealt with a stiffness fitting transformation in a single time step. The particles on the overlap region belong to multiple clusters. Larger scale deformation effects were simulated by multiple rotation transformations. Finally, the weighting scheme based on the inverse distance square kernel was used to calculate the qualities of the particles on the overlapping region. The mass proportion was reasonably allocated according to the distance between the particles and the cluster, and then the cluster center was updated. The weight and the centroid of each cluster was updated in time, the large offset of the particles in the partitioning process was effectively avoided. The experimental results show that the random clustering can quickly divide the particle clusters in any model and allow to simulate large-scale elastic deformations. The combination of the random clustering and the shape matching has strong robustness as well as real-time performance, which is more suitable for interactive simulations.
Aiming at the problem that the traditional shape matching method is limited to small deformation simulation, a partitioning method based on random clustering was proposed. Firstly, the solution of the traditional rotation matrix was optimized. And the position constraint factor was introduced to re-correct the target position to avoid the penetration phenomenon. Secondly, a random clustering strategy was used to divide the particle clusters to generate a series of overlapping clusters. Each cluster was dealt with a stiffness fitting transformation in a single time step. The particles on the overlap region belong to multiple clusters. Larger scale deformation effects were simulated by multiple rotation transformations. Finally, the weighting scheme based on the inverse distance square kernel was used to calculate the qualities of the particles on the overlapping region. The mass proportion was reasonably allocated according to the distance between the particles and the cluster, and then the cluster center was updated. The weight and the centroid of each cluster was updated in time, the large offset of the particles in the partitioning process was effectively avoided. The experimental results show that the random clustering can quickly divide the particle clusters in any model and allow to simulate large-scale elastic deformations. The combination of the random clustering and the shape matching has strong robustness as well as real-time performance, which is more suitable for interactive simulations.
引文
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[2]Sifakis E,Barbi?J.FEM simulation of 3D deformable solids:a practitioner’s guide to theory,discretization and model reduction[C]//Proceedings of International Conference on Computer Graphics and Interactive Techniques.New York:ACM Press,2012:Article No.20
[3]Zhao Jing,Tang Yong,Li Sheng,et al.Survey on the application and design of material constitutive model for deformable solid simulation[J].Journal of Software,2017,28(9):2502-2523(in Chinese)(赵静,唐勇,李胜,等.形变体仿真中材质本构模型的应用与设计综述[J].软件学报,2017,28(9):2502-2523)
[4]Zhao Jing,Tang Yong,Li Sheng,et al.Efficient example-based material simulation in Laplace-Beltrami shape space[J].Journal of Computer-Aided Design&Computer Graphics,2017,29(9):1681-1688(in Chinese)(赵静,唐勇,李胜,等.利用Laplace-Beltrami形状空间的基于样例材料的快速仿真方法[J].计算机辅助设计与图形学学报,2017,29(9):1681-1688)
[5]Müller M,Chentanez N.Solid simulation with oriented particles[J].ACM Transactions on Graphics,2011,30(4):Article No.92
[6]Müller M,Heidelberger B,Teschner M,et al.Meshless deformations based on shape matching[J].ACM Transactions on Graphics,2005,24(3):471-478
[7]Rivers A R,James D L.FastLSM:fast lattice shape matching for robust real-time deformation[J].ACM Transactions on Graphics,2007,26(3):Article No.82
[8]Steinemann D,Otaduy M A,Gross M.Fast adaptive shape matching deformations[C]//Proceedings of the ACM SIGGR-APH/Eurographics Symposium on Computer Animation.Airela-Ville:Eurographics Association Press,2008:87-94
[9]Diziol R,Bender J,Bayer D.Robust real-time deformation of incompressible surface meshes[C]//Proceedings of the ACMSIGGRAPH/Eurographics Symposium on Computer Animation.New York:ACM Press,2011:237-246
[10]Bargteil A W,Jones B.Strain limiting for clustered shape matching[C]//Proceedings of the 7th International Conference on Motion in Games.New York:ACM Press,2014:177-179
[11]Jones B,Martin A,Levine J A,et al.Clustering and collision detection for clustered shape matching[C]//Proceedings of the8th ACM SIGGRAPH Conference on Motion in Games.New York:ACM Press,2015:199-204
[12]Jones B,Martin A,Levine J A,et al.Ductile fracture for clustered shape matching[C]//Proceedings of the 20th ACMSIGGRAPH Symposium on Interactive 3D Graphics and Games.New York:ACM Press,2016:65-70
[13]Jones B,Ward S,Jallepalli A,et al.Deformation embedding for point-based elastoplastic simulation[J].ACM Transactions on Graphics,2014,33(2):Article No.21
[14]Falkenstein M,Jones B,Levine J A,et al.Reclustering for large plasticity in clustered shape matching[C]//Proceedings of the 10th International Conference on Motion in Games.New York:ACM Press,2017:Article No.5
[15]Tang Yong,Yang Sisi,Lyu Mengya,et al.Collision detection for cloth based on adaptive enclosing ellipsoids[J].Journal of Computer-Aided Design&Computer Graphics,2013,25(10):1589-1596(in Chinese)(唐勇,杨偲偲,吕梦雅,等.自适应椭球包围盒改进织物碰撞检测方法[J].计算机辅助设计与图形学学报,2013,25(10):1589-1596)
[16]Irving G,Teran J,Fedkiw R.Invertible finite elements for robust simulation of large deformation[C]//Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation.Aire-la-Ville:Eurographics Association Press,2004:131-140
[17]Müller M,Heidelberger B,Hennix M,et al.Position based dynamics[J].Journal of Visual Communication and Image Representation,2007,18(2):109-118
[18]Wang H M,Yang Y.Descent methods for elastic body simulation on the GPU[J].ACM Transactions on Graphics,2016,35(6):Article No.212
[19]Zhu F,Zhao J,Li S,et al.Dynamically enriched MPM for invertible elasticity[J].Computer Graphics Forum,2017,36(6):381-392
[20]Chentanez N,Müller M,Macklin M.Real-time simulation of large elasto-plastic deformation with shape matching[C]//Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation.Aire-la-Ville:Eurographics Association Press,2016:159-167
[21]Liu T T,Bargteil A W,O’Brien J F,et al.Fast simulation of mass-spring systems[J].ACM Transactions on Graphics,2013,32(6):Article No.214
[22]Bouaziz S,Martin S,Liu T T,et al.Projective dynamics:fusing constraint projections for fast simulation[J].ACM Transactions on Graphics,2014,33(4):Article No.154