A Finite Element Method for Interactive Physically Based Shape Modelling with Quadratic Tetrahedra

Abstract

We present an alternative approach to standard geometric shape editing using physically-based simulation. With our technique, the user can deform complex objects in real-time. The enabling technology of this approach is a fast and accurate finite element implementation of an elasto-plastic material model, specifically designed for interactive shape manipulation. Using quadratic shape functions, we avoid the inherent drawback of volume locking exhibited by methods based on linear finite elements. The physical simulation uses a tetrahedral mesh, which is constructed from a coarser approximation of the detailed surface. Having computed a deformed state of the tetrahedral mesh, the deformation is transferred back to the high detail surface. This can be accomplished in an accurate and efficient way using the quadratic shape functions. In order to guarantee stability and real-time frame rates during the simulation, we cast the elasto-plastic problem into a linear formulation. For this purpose, we present a corotational formulation for quadratic finite elements. We demonstrate the versatility of our approach in interactive manipulation sessions and show that our animation system can be coupled with further physics-based animations like, e.g. fluids and cloth, in a bi-directional way.