Hierarchical Clustering for Enhanced Elastic Behavior in Clustered Shape Matching

Abstract

One of many popular approaches for physics-based animation of deformable objects is clustered shape matching. In this approach, each object is broken into overlapping clusters of particles. At each timestep, a best-fit rigid transformation between the object's rest state and current particle configuration is computed, and Hookean springs are used to pull particles towards the desired goal positions. In this theses, we present hierarchical clustering as a novel extension to the clustered shape matching approach. In our methodology, we construct a hierarchy of fine-to-coarse sets of clusters over the set of particles and compute weighted particle dynamics. We hypothesize that our approach enhances elastic behavior and provides a good blend of stiffness and richness in deformation, which are in contention in the traditional clustered shape matching approach. We include several examples in this theses to support our hypotheses and demonstrate the versatility of our approach.