BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics

Abstract We propose BlendSim, a novel framework for editable simulation using spacetime optimization on the lightweight animation representation. Traditional spacetime control methods suffer from a high computational complexity, which limits their use in interactive animation. The proposed approach effectively reduces the dimensionality of the problem by representing the motion trajectories of each vertex using continuous parametric Bézier splines with variable keyframe times. Because this mesh animation representation is continuous and fully differentiable, it can be optimized such that it follows the laws of physics under various constraints. The proposed method also integrates constraints, such as collisions and cyclic motion, making it suitable for real‐world applications where seamless looping and physical interactions are required. Leveraging projective dynamics, we further enhance the computational efficiency by decoupling the optimization into local parallelizable and global quadratic steps, enabling a fast and stable simulation. In addition, BlendSim is compatible with modern animation workflows and file formats, such as the glTF, making it practical way for authoring and transferring mesh animation.