Alvin Shi, Haomiao Wu, Theodore Kim
We present a method for simulating deformable bodies in four spatial dimensions. To accomplish this, we generalize several pieces of the traditional simulation pipeline. Starting from the meshing stage, we propose a simple method for generating a pentachoral mesh, the 4D analog of a tetrahedral mesh. Next, we show how to generalize the deformation invariants, allowing us to construct 4D hyperelastic energies that lead directly to hyper-dimensional deformation forces. Finally, we formulate collision detection and response in 4D. Our eigenanalyses of the resulting deformation and collision energies generalize to arbitrarily higher dimensions. The resulting simulations display a variety of previously unseen visual phenomena.