Example-based elastic materials

MartinSebastian,; ThomaszewskiBernhard,; GrinspunEitan,; GrossMarkus,

doi:10.1145/2010324.1964967

Cited by 149 publications

(94 citation statements)

References 6 publications

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“…Our method works robustly with fixed timestep even if only a few iterations of the local/global solver are enabled. In most of our examples we use h = 1/30s and compare our technique to a robust numerical implementation of Newton's method that employs a line search scheme and diagonal Hessian correction in the case of indefinite matrices [Martin et al 2011]. Note that our method does not require any such precautions-both the local and global steps find the exact minimum in their subsets of variables, so no line search is necessary.…”

Section: Resultsmentioning

confidence: 99%

“…A related time-stepping strategy involves the combination of implicit and explicit methods (IMEX) [Bridson et al 2003;Stern and Grinspun 2009]. However, numerical damping may be tolerable in applications where energy conservation is not critical and many recent methods continue to rely on the implicit Euler method [Martin et al 2011;Hahn et al 2012]. A recently proposed technique that allows for a more direct control of damping is energy budgeting [Su et al 2013].…”

Section: Related Workmentioning

confidence: 99%

“…(7). This leads to the optimization problem minx g(x); this formulation is known as variational implicit Euler [Martin et al 2011]. To avoid confusion with symplectic methods (sometimes also called variational [Stern and Desbrun 2006]), we will refer to eq.…”

Section: Background and Notationmentioning

confidence: 99%

“…(8) as optimization implicit Euler. The standard numerical solution of the optimization implicit Euler also employs Newton's method [Martin et al 2011]. …”

Section: Background and Notationmentioning

confidence: 99%

“…We consider the optimization formulation of implicit Euler integration [Martin et al 2011], where time-stepping is cast as a minimization problem. Our method works well with large timesteps-most of our examples assume a fixed timestep corresponding to the framerate, i.e., h = 1/30s.…”

Section: Introductionmentioning

confidence: 99%

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Fast simulation of mass-spring systems

et al. 2013

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We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton's method. Although the asymptotic convergence of Newton's method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton's. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton's iteration. AbstractWe describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. This scheme provides a fast solution for classical linear (Hookean) springs. We express the widely used implicit Euler method as an energy minimization problem and introduce spring directions as auxiliary unknown variables. The system is globally linear in the node positions, and the non-linear terms involving the directions are strictly local. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. Our method converges to the same final result as would be obtained by solving the standard form of implicit Euler using Newton's method. Although the asymptotic convergence of Newton's method is faster than ours, the initial ratio of work to error reduction with our method is much faster than Newton's. For real-time visual applications, where speed and stability are more important than precision, we obtain visually acceptable results at a total cost per timestep that is only a fraction of that required for a single Newton iteration. When higher accuracy is required, our algorithm can be used to compute a good starting point for subsequent Newton's iteration.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Background and Notationmentioning

confidence: 99%

“…(8) as optimization implicit Euler. The standard numerical solution of the optimization implicit Euler also employs Newton's method [Martin et al 2011]. …”

Section: Background and Notationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast simulation of mass-spring systems

et al. 2013

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Dynamic sprites: artistic authoring of interactive animations

Jones

McCann

et al. 2014

Computer Animation & Virtual

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Traditional methods for creating dynamic objects and characters from static drawings involve careful tweaking of animation curves and/or simulation parameters. Sprite sheets offer a more drawing-centric solution, but they do not encode timing information or the logic that determines how objects should transition between poses and cannot generalize outside the given drawings. We present an approach for creating dynamic sprites that leverages sprite sheets while addressing these limitations. In our system, artists create a drawing, deform it to specify a small number of example poses, and indicate which poses can be interpolated. To make the object move, we design a procedural simulation to navigate the pose manifold in response to external or user-controlled forces. Powerful artistic control is achieved by allowing the artist to specify both the pose manifold and how it is navigated, while physics is leveraged to provide timing and generality. We used our method to create sprites with a range of different dynamic properties.

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Enhanced rig‐space simulation

Ouyang

Wei

et al. 2016

Computer Animation & Virtual

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Rig-space physics a finite element method(FEM) based simulation technique that aims at adding secondary motion on a character while maintaining seamless cooperation with traditional animation pipelines. We enhance the rig-space physics by introducing several techniques, including general field interaction, proportional-derivative control, and improved material control. This allows an animator to perform various interferences to the simulation process and create more abundant animation effects. Moreover, we also improve the numerical stability of the simulation algorithm by prepending a conjugate gradient procedure.

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Example-based elastic materials

Cited by 149 publications

References 6 publications

Fast simulation of mass-spring systems

Fast simulation of mass-spring systems

Dynamic sprites: artistic authoring of interactive animations

Enhanced rig‐space simulation

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