• Corpus ID: 15618295

Proofs of two Theorems concerning Sparse Spacetime Constraints

@article{Schulz2014ProofsOT,
  title={Proofs of two Theorems concerning Sparse Spacetime Constraints},
  author={Christian Schulz and Christoph von Tycowicz and Hans-Peter Seidel and Klaus Hildebrandt},
  journal={ArXiv},
  year={2014},
  volume={abs/1405.1902}
}
In the SIGGRAPH 2014 paper [SvTSH14] an approach for animating deformable objects using sparse spacetime constraints is introduced. This report contains the proofs of two theorems presented in the paper. 

Animating deformable objects using sparse spacetime constraints

A scheme for animating deformable objects based on spacetime optimization that robustly and within a few seconds generates interesting motion from a sparse set of spacetime constraints.

References

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Animating deformable objects using sparse spacetime constraints

A scheme for animating deformable objects based on spacetime optimization that robustly and within a few seconds generates interesting motion from a sparse set of spacetime constraints.

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An interactive approach to generate physically based shape interpolation between poses to offer an efficient and robust numerical technique to generate physical-plausible dynamics even for very large deformation.

Spacetime constraints

This work presents as examples a Luxo lamp performing a variety of coordinated motions that conform to such principles of traditional animation as anticipation, squash-and-stretch, follow-through, and timing.

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This work presents a fast space-time optimization method to author physically based deformable object simulations that conform to animator-specified keyframes and demonstrates the method with FEM deformable objects and mass-spring systems.

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This direct editing tool can serve the final stages of animation production, which often call for detailed, direct adjustments that are otherwise tedious to realize by re-simulation or frame-by-frame editing.

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The Wiggly Spline makes it possible to canonicalize a simulation, generalize it by providing frequency and damping controls and control it through direct manipulation, as well as provide a combination of direct manipulation and physical realism.