Discrete representation of elastic bodies for physical simulation

Simulation of elastic objects has received a lot of attention in the past decade in the computer graphics community, due to their ubiquity and importance in our everyday life; some examples include muscles, squishy balls, cloth, and many more. When approaching physical simulation, the computer graphics community has focused on the questions on the representation of 3D data, for example, by building a theory of discrete differential geometry to represent nonlinear deformation, and by inventing algorithms to reconstruct and simulate digital twins of real-world elastic objects. Despite the extensive research, there is not a unified solution that integrates the discrete geometric understanding in the graphics research and combines it with the sophisticated physical modelling in scientific computing. This thesis explores possibilities to bridge the gap between graphics and computational physics by taking the state-of-the-art computer graphics algorithms for representing and discretizing 3D geometry and deformations and equipping these discrete geometric models with physics.