Progressing Level-of-Detail Animation of Volumetric Elastodynamics

Abstract: We extend the progressive dynamics model (Zhang et al., 2024) from cloth and shell simulation to volumetric finite elements, enabling an efficient level-of-detail (LOD) animation-design pipeline with predictive coarse-resolution previews facilitating rapid iterative design for a final, to-be-generated, high-resolution animation of volumetric elastodynamics. This extension to volumetric domains poses significant new challenges, including the construction of suitable mesh hierarchies and the definition of effective prolongation operators for codimension-0 progressive dynamics. To address these challenges, we propose a practical method for defining multiresolution hierarchies and, more importantly, introduce a simple yet effective topology-aware algorithm for constructing prolongation operators between overlapping (but not necessarily conforming) volumetric meshes. Our key insight is a boundary binding strategy that enables the computation of barycentric coordinates, allowing several off-the-shelf interpolants -- such as standard barycentric coordinates, Biharmonic Coordinates (Wang et al., 2015), and Phong Deformation (James, 2020) -- to serve as "plug-and-play" components for prolongation with minimal modification. We show that our progressive volumetric simulation framework achieves high-fidelity matching LOD animation across resolutions including challenging dynamics with high speeds, large deformations, and frictional contact.