Multi-resolution Clustering for Enhanced Elastic Behavior in Clustered Shape Matching

Abstract

Clustered shape matching is an approach for physics-based animation of deformable objects, which breaks an object into overlapping clusters of particles. At each timestep, it computes a best-fit rigid transformation between a cluster's rest state and current particle configuration and Hookean springs are used to pull particles toward desired goal positions. In this paper, we present multi-resolution clustering as an extension to clustered shape matching. We iteratively construct fine-to-coarse sets of clusters and weights over the set of particles and compute dynamics in a single coarse-to-fine pass. We demonstrate that our approach enhances the possible elastic behavior available to artists and provides an intuitive parameterization to blend between stiffness and deformation richness, which are in contention in the traditional clustered shape matching approach that operates at a single spatial scale. We can specify a different stiffness value for each resolution level, where a greater weight at coarser levels result in a stiffer object while a greater weight at finer levels yield richer deformation; we evaluate a number of approaches for choosing these stiffness values and demonstrate the differences in the accompanying video.