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吕梦雅, 任小霞, 赵静, 刘宇涵, 贾江凯, 赵伟, 唐勇. 随机聚类形状匹配的形变体实时仿真[J]. 计算机辅助设计与图形学学报, 2019, 31(7): 1229-1237. DOI: 10.3724/SP.J.1089.2019.17444
引用本文: 吕梦雅, 任小霞, 赵静, 刘宇涵, 贾江凯, 赵伟, 唐勇. 随机聚类形状匹配的形变体实时仿真[J]. 计算机辅助设计与图形学学报, 2019, 31(7): 1229-1237. DOI: 10.3724/SP.J.1089.2019.17444
Lyu Mengya, Ren Xiaoxia, Zhao Jing, Liu Yuhan, Jia Jiangkai, Zhao Wei, Tang Yong. Real-Time Simulation of Deformable Solids with Random Cluster Shape Matching[J]. Journal of Computer-Aided Design & Computer Graphics, 2019, 31(7): 1229-1237. DOI: 10.3724/SP.J.1089.2019.17444
Citation: Lyu Mengya, Ren Xiaoxia, Zhao Jing, Liu Yuhan, Jia Jiangkai, Zhao Wei, Tang Yong. Real-Time Simulation of Deformable Solids with Random Cluster Shape Matching[J]. Journal of Computer-Aided Design & Computer Graphics, 2019, 31(7): 1229-1237. DOI: 10.3724/SP.J.1089.2019.17444

随机聚类形状匹配的形变体实时仿真

Real-Time Simulation of Deformable Solids with Random Cluster Shape Matching

  • 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.

     

    Abstract: 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.

     

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