Reclustering for large plasticity in clustered shape matching

In this paper, we revisit the problem online reclustering in clustered shape matching simulations and propose an approach that employs two nonlinear optimizations to create new clusters. The first optimization finds the embedding of particles and clusters into three-dimensional space that minimizes elastic energy. The second finds the optimal location for the new cluster, working in this embedded space. The result is an approach that is more robust in the presence of elastic deformation. We also experimentally verify that our clustered shape matching approach converges as the number of clusters increases, suggesting that our reclustering approach does not change the underlying material properties. Further, we demonstrate that particle resampling is not strictly necessary in our framework allowing us to trivially conserve volume. Finally, we highlight an error in estimating rotations in the original shape-matching work [Müller et al. 2005] that has been repeated in much of the follow up work.