High-Order Elements in Position Based Dynamics

Abstract: The simulation of deformable objects has been the subject of a great deal of work in the field of computer graphics. The constraint-based PBD (Position-Based Dynamics) approach has been proven to be effective in this field for real-time and stable deformable objects simulation. Finite element method with linear tetrahedron discretization is the most widely used in computer graphics despite producing less accurate results than hexahedral or higher-order elements. In this context, our proposal is to integrate higher degree elements within the PBD framework. In addition, we propose a solution to improve convergence of unstable energies (like Neo-Hooke) when used as constraints. We show that our approach improves accuracy compared to linear tetrahedra. We also highlight the time savings, since fewer elements are needed.

Keywords: Physical based simulation; Position-based dynamics; High-order elements; Elasticity; Real-time physics