Interactive editing of deformable simulations

Space-time editing of elastic motion through material optimization and reduction

“…Recently, a number of methods has been proposed to control elastic object animation as it represents a challenge in both geometry processing and animation. While pose (or keyframe) interpolation has been shown a useful tool [Barbič et al 2009;Huang et al 2011;Hildebrandt et al 2012], the framework of space-time constraints [Witkin and Kass 1988;Fang and Pollard 2003;Safonova et al 2004;Jeon and Choi 2007;Barbič et al 2012;Li et al 2013] offers a more general approach to intuitively edit an input sequence: editing is cast as a constrained optimal control problem, in which one solves for the least amount of non-physical forces needed to satisfy user-defined constraints in space and time.…”

“…This issue was circumvented in the context of pose interpolation by either applying linearization around the keyframes [Hildebrandt et al 2012] or introducing a Rotation-Strain (RS) space [Huang et al 2011]; alas, these solutions do not address the general case of space-time and partial positional constraints. Still, some alternatives were proposed: Barbič et al [2012] used [Huang et al 2011] in a post-warping step, at the cost of violating position constraints; linearizing the equation of motion around the input trajectory [Barbič and Popović 2008;Li et al 2013] often achieves tighter position constraints, but artifacts still appear when large motion editing is performed.…”

“…However, the same equation and modal analysis can be applied more generally for any animation sequence. When editing an existing sequenceū(t), for instance, we seek an offset u(t) that makes the final animationū(t)+u(t) satisfy user-specified space-time constraints through the least amount of control forces [Barbič et al 2012;Li et al 2013]. In the case of keyframe interpolation, we instead setū as a rest shape and consider it constant in time.…”

“…From the input sequence given as positionsū(t) of nodes in time, one could find an optimal offset u(t) to the input sequence that satisfies user-specified constraints as in [Barbič et al 2012;Li et al 2013] with least control force, and reconstruct the shape throughū(t)+u(t). However, such a linearized scheme leads to significant artifacts if large offsets are needed, and even the use of post-warping [Barbič et al 2012] to mitigate these effects often incurs violation of position constraints. Instead, RS coordinates offer dramatic improvement to the editing process even for constraints involving large offsets.…”

“…Fig. 5 shows a comparison of our methods versus [Barbič et al 2012]. We use as input a steady animation in which each frame is the rest shape of a flower, with properly scaled uniform material parameters.…”