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

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.