In this paper, we present a strategy to decrease the computational demands of the Small Steps Method in Projective Dynamics, which serves to simulate elastic bodies. The balance between simulation quality and computational effort remains a persistent challenge in computer graphics (CG) for interactive environments. By subdividing the time progression into minor segments rather than halting the iterative process prematurely, the Small Steps Method enhances simulations by diminishing numerical damping.
It’s important to acknowledge that the small-step approach presupposes the calculation of intermediate steps that are not visually represented, thereby eliminating temporal redundancies. We specifically introduce the DummyStep, an advanced Euler method that utilizes acceleration for temporal development, replacing half of the substeps in Projective Dynamics with DummyStep. Consequently, the Dummy Steps Method can supplant the Small Steps Method with minimal error, halving the computational complexity.
Nevertheless, the Dummy Steps Method experiences certain stability issues. Therefore, we suggest two adjustments to bolster the method’s stability. Through various examples, we illustrate that our proposed method can consistently supplant the small-step approach while substantially diminishing computational demands.