Jia, ShiyangWang, StephanieLi, Tzu-MaoChern, AlbertWang, HuaminYe, YutingVictor Zordan2023-10-162023-10-1620232577-6193https://doi.org/10.1145/3606938https://diglib.eg.org:443/handle/10.1145/3606938We address the problem of synthesizing physical animations that can loop seamlessly. We formulate a variational approach by deriving a physical law in a periodic time domain. The trajectory of the animation is represented as a parametric closed curve, and the physical law corresponds to minimizing the bending energy of the curve. Compared to traditional keyframe animation approaches, our formulation is constraint-free, which allows us to apply a standard Gauss–Newton solver. We further propose a fast projection method to efficiently generate an initial guess close to the desired animation. Our method can handle a variety of physical cyclic animations, including clothes, soft bodies with collisions, and N-body systems.CCS Concepts: Computing methodologies -> Physical simulation keyframe animation, periodic motion, physical simulation"Computing methodologiesPhysical simulation keyframe animationperiodic motionphysical simulation"10.1145/3606938