Figure 1: From an input sequence (bottom) of a standing T. rex simulated via a Saint Venant-Kirchhoff deformation model, we edit the input motion with 27 space-time constraints to make the dinosaur squat & jump while trying to catch the small plane flying around it (top). AbstractWe present a novel method for elastic animation editing with spacetime constraints. In a sharp departure from previous approaches, we not only optimize control forces added to a linearized dynamic model, but also optimize material properties to better match user constraints and provide plausible and consistent motion. Our approach achieves efficiency and scalability by performing all computations in a reduced rotation-strain (RS) space constructed with both cubature and geometric reduction, leading to two orders of magnitude improvement over the original RS method. We demonstrate the utility and versatility of our method in various applications, including motion editing, pose interpolation, and estimation of material parameters from existing animation sequences.

We present an intuitive and interactive approach for motion editing through space–time constraints on positions. Given an input motion of an elastic body, our approach enables the user to interactively edit node positions in order to alter and fine‐tune the motion. We formulate our motion editing as an optimization problem with dynamics constraints to enforce a physically plausible result. Through linearization of the editing around the input trajectory, we simplify this constrained optimal control problem into an unconstrained quadratic optimization. The optimal motion thus becomes the solution of a dense linear system, which we solve efficiently by applying the adjoint method in each iteration of a conjugate gradient solver. We demonstrate the efficiency and quality of our motion editing technique on a series of examples. Copyright © 2013 John Wiley & Sons, Ltd.

We present a stable and efficient simulator for deformable objects with collisions and contacts. For stability, an optimization derived from the implicit time integrator is solved in each timestep under the inequality constraints coming from collisions. To achieve fast convergence, we extend the MPRGP based solver from handling box constraints only to handling general linear constraints and prove its convergence. This generalization introduces a cost of solving dense linear systems in each step, but these systems can be reduced into diagonal ones for efficiency without affecting the general stability via pruning redundant collisions. Our solver is an order of magnitude faster, especially for elastic objects under large deformation compared with iterative constraint anticipation method (ICA), a typical method for stability. The efficiency, robustness and stability are further verified by our results.

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