TY - JOUR A1 - Schulz, Christian A1 - Tycowicz, Christoph von A1 - Seidel, Hans-Peter A1 - Hildebrandt, Klaus T1 - Animating Deformable Objects Using Sparse Spacetime Constraints T2 - ACM Transactions on Graphics N2 - We propose a scheme for animating deformable objects based on spacetime optimization. The main feature is that it robustly and quickly (within a few seconds) generates interesting motion from a sparse set of spacetime constraints. Providing only partial (as opposed to full) keyframes for positions and velocities is sufficient. The computed motion satisfies the constraints and the remaining degrees of freedom are determined by physical principles using elasticity and the spacetime constraints paradigm. Our modeling of the spacetime optimization problem combines dimensional reduction, modal coordinates, wiggly splines, and rotation strain warping. Controlling the warped motion requires the derivative of the warp map. We derive a representation of the derivative that can be efficiently and robustly evaluated. Our solver is based on a theorem that characterizes the solutions of the optimization problem and allows us to restrict the optimization to very low-dimensional search spaces. This treatment of the optimization problem avoids a time discretization and the resulting method can robustly deal with sparse input and wiggly motion. Y1 - 2014 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/5452 VL - 33 IS - 4 SP - 109:1 EP - 109:10 ER -