November 2012 – Physics-Based Animation

Jonathan R. Bronson, Joshua A. Levine, Ross T. Whitaker

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, in order to reduce element counts in regions of homogeneity.

Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality

Fun Shing Sin, Daniel Schroeder, Jernej Barbic

This practice and experience paper describes a robust C++ implementation of several non-linear solid three-dimensional deformable object strategies commonly employed in computer graphics, named the Vega finite element method (FEM) simulation library. Deformable models supported include co-rotational linear FEM elasticity, Saint–Venant Kirchhoff FEM model, mass–spring system and invertible FEM models: neo-Hookean, Saint–Venant Kirchhoff and Mooney–Rivlin. We provide several timestepping schemes, including implicit Newmark and backward Euler integrators, and explicit central differences. The implementation of material models is separated from integration, which makes it possible to employ our code not only for simulation, but also for deformable object control and shape modelling. We extensively compare the different material models and timestepping schemes. We provide practical experience and insight gained while using our code in several computer animation and simulation research projects.

Vega: Non-Linear FEM Deformable Object Simulator