ESBD: Exponential Strain-based Dynamics using XPBD algorithm

Strain-based Dynamics (SBD) (Muller et al., 2014) is a well-known method to simulate the deformable models by using Green's strain tensor within the Position-based Dynamics (PBD) algorithm. Similar to the other position-based constraints, SBD performs stable and robust. However, when we transform the base algorithm from PBD to Extended Position-based Dynamics (XPBD), SBD suffers from the cumbersome parameter adjustments and uncontrollable numerical dissipation, which generates highly stiff results. To overcome these limitations, we propose Exponential Strain-based Dynamics (ESBD) which reformulates the Green's strain tensor with an exponential treatment. Our proposed method is less sensitive to the increased numerical dissipation, so it provides vivid simulation of deformable objects with fewer parameter tunings. In order to present the advantages, we compare our method with SBD by using the XPBD method and other well-known techniques. We observe that ESBD improves the hyperelastic behavior of the Green's strain tensor as a projected constraint without altering the underlying XPBD algorithm. Therefore, it is possible to adapt ESBD to the other existing numerical integration and iteration methods. Our proposed method is stable, straightforward to follow and produces high quality dynamic simulations.