@article{SchulzTycowiczSeideletal., author = {Schulz, Christian and Tycowicz, Christoph von and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {Animating Deformable Objects Using Sparse Spacetime Constraints}, series = {ACM Transactions on Graphics}, volume = {33}, journal = {ACM Transactions on Graphics}, number = {4}, doi = {10.1145/2601097.2601156}, pages = {109:1 -- 109:10}, abstract = {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.}, language = {en} } @article{TycowiczSchulzSeideletal., author = {Tycowicz, Christoph von and Schulz, Christian and Seidel, Hans-Peter and Hildebrandt, Klaus}, title = {An Efficient Construction of Reduced Deformable Objects}, series = {ACM Transactions on Graphics}, volume = {32}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {ACM}, doi = {10.1145/2508363.2508392}, pages = {213:1 -- 213:10}, abstract = {Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for real-time simulation of deformable objects and interactive deformation-based editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches.}, language = {en} }