SCA 14: Eurographics/SIGGRAPH Symposium on Computer Animation

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https://diglib.eg.org/handle/10.2312/7760

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Adaptive Tetrahedral Meshes for Brittle Fracture Simulation
(The Eurographics Association, 2014) Koschier, Dan; Lipponer, Sebastian; Bender, Jan; Vladlen Koltun and Eftychios Sifakis
We present a method for the adaptive simulation of brittle fracture of solid objects based on a novel reversible tetrahedral mesh refinement scheme. The refinement scheme preserves the quality of the input mesh to a large extent, it is solely based on topological operations, and does not alter the boundary, i.e. any geometric feature. Our fracture algorithm successively performs a stress analysis and increases the resolution of the input mesh in regions of high tensile stress. This results in an accurate location of crack origins without the need of a general high resolution mesh which would cause high computational costs throughout the whole simulation. A crack is initiated when the maximum tensile stress exceeds the material strength. The introduced algorithm then proceeds by iteratively recomputing the changed stress state and creating further cracks. Our approach can generate multiple cracks from a single impact, but effectively avoids shattering artifacts. Once the tensile stress decreases, the mesh refinement is reversed to increase the performance of the simulation. We demonstrate that our adaptive method is robust, scalable and computes highly realistic fracture results.
An Adaptive Virtual Node Algorithm with Robust Mesh Cutting
(The Eurographics Association, 2014) Wang, Yuting; Jiang, Chenfanfu; Schroeder, Craig; Teran, Joseph; Vladlen Koltun and Eftychios Sifakis
We present a novel virtual node algorithm (VNA) for changing tetrahedron mesh topology to represent arbitrary cutting triangulated surfaces. Our approach addresses a number of shortcomings in the original VNA of [MBF04]. First, we generalize the VNA so that cuts can pass through tetrahedron mesh vertices and lie on mesh edges and faces. The original algorithm did not make sense for these cases and required often ambiguous perturbation of the cutting surface to avoid them. Second, we develop an adaptive approach to the definition of embedded material used for element duplication. The original algorithm could only handle a limited number of configurations which restricted cut surfaces to have curvature at the scale of the tetrahedron elements. Our adaptive approach allows for cut surfaces with curvatures independent of the embedding tetrahedron mesh resolution. Finally, we present a novel, provably-robust floating point mesh intersection routine that accurately registers triangulated surface cuts against the background tetrahedron mesh without the need for exact arithmetic.
Fast Grid-Based Nonlinear Elasticity for 2D Deformations
(The Eurographics Association, 2014) Setaluri, Rajsekhar; Wang, Yu; Mitchell, Nathan; Kavan, Ladislav; Sifakis, Eftychios; Vladlen Koltun and Eftychios Sifakis
We present a deformation technique that constructs 2D warps by using spline curves to specify the starting and target shapes of selected key contours. We generate a two-dimensional deformation map from these contours by simulating a non-linear elastic membrane deforming in accordance with user-specified constraints. Although we support and demonstrate elastic models inspired by physical membranes, we highlight a custom material model for this specific application, which combines the benefits of harmonic interpolation and area-preserving deformations. Our warps are represented via a standard Cartesian lattice and leverage the regularity of this description to enable efficient computation. Specifically, our method resolves the targeting constraints imposed along arbitrarily shaped contours with sub-grid cell precision, without requiring an explicit remeshing of the warp lattice around the constraint curve. We describe how to obtain a well-conditioned discretization of our membrane model even under elaborate constraints and strict area preservation demands, and present a multigrid solver for the efficient numerical solution of the deformation problem.
A Peridynamic Perspective on Spring-Mass Fracture
(The Eurographics Association, 2014) Levine, Joshua A.; Bargteil, Adam W.; Corsi, Christopher; Tessendorf, Jerry; Geist, Robert; Vladlen Koltun and Eftychios Sifakis
The application of spring-mass systems to the animation of brittle fracture is revisited. The motivation arises from the recent popularity of peridynamics in the computational physics community. Peridynamic systems can be regarded as spring-mass systems with two specific properties. First, spring forces are based on a simple strain metric, thereby decoupling spring stiffness from spring length. Second, masses are connected using a distancebased criterion. The relatively large radius of influence typically leads to a few hundred springs for every mass point. Spring-mass systems with these properties are shown to be simple to implement, trivially parallelized, and well-suited to animating brittle fracture.
Steklov-Poincaré Skinning
(The Eurographics Association, 2014) Gao, Ming; Mitchell, Nathan; Sifakis, Eftychios; Vladlen Koltun and Eftychios Sifakis
We introduce a novel and efficient simulation technique for generating physics-based skinning animations of skeleton-driven characters with full support for collision handling. Although physics-based approaches may use a volumetric (e.g. tetrahedral) flesh model, operations such as rendering, collision processing and user manipulation directly involve only the surface of this mesh. Motivated by this fact we define an elastic model of the skin surface which, while directly using only the surface degrees of freedom, exhibits a mechanical response that captures the full volumetric flesh behavior. We achieve this unusual result by combining three fundamental contributions: First, we present a material model which offers a plausible approximation to corotational elasticity at significantly reduced cost, by computing local rotations via procedural skinning rather than deriving them from the mesh deformation; the result is a force model which is affine on vertex positions, with coefficients dependent on the skeletal pose (but not on the deformation). Second, we use this force model to derive a direct mapping between surface vertex positions and resulting equilibrium forces on the same boundary vertices, which is a discrete version of the Steklov-Poincaré operator of the volumetric elastic model. This mapping is conveniently shown to also be affine (with pose-dependent coefficients), but with a dense stiffness matrix which renders direct numerical solution impractical. However, as a third and final step we show how a modified Newton iteration and a skinninginspired preconditioner can solve the boundary problem with a competitive runtime cost. We assess the efficacy of our solution in simulations of high resolution human flesh models, with full external and self-collision processing.
Strain Based Dynamics
(The Eurographics Association, 2014) Müller, Matthias; Chentanez, Nuttapong; Kim, Tae-Yong; Macklin, Miles; Vladlen Koltun and Eftychios Sifakis
We propose a new set of constraints within the Position Based Dynamics (PBD) framework that allow the control of strain in directions that are independent of the edge directions of the simulation mesh. Instead of constraining distances between points, we constrain the entries of the Green - St Venant strain tensor. Varying the stiffness values corresponding to the individual strain coefficients lets us simulate anisotropic behavior. By working with Green's rotation-independent, non-linear strain tensor directly we do not have to perform a polar decomposition of the deformation gradient as in most strain limiting approaches. In addition, we propose a modification of the constraints corresponding to the diagonal entries of the strain tensor such that they can be solved in a single step and a modification of the constraints corresponding to the off-diagonal entries to decouple stretch from shear resistance. By formulating the constraints within the PBD framework, they can be used not only for strain limiting but to perform the actual simulation of the deformable object whereas traditional strain limiting methods have to be paired with a separate simulation method.
View-Dependent Adaptive Cloth Simulation
(The Eurographics Association, 2014) Koh, Woojong; Narain, Rahul; O'Brien, James F.; Vladlen Koltun and Eftychios Sifakis
This paper describes a method for view-dependent cloth simulation using dynamically adaptive mesh refinement and coarsening. Given a prescribed camera motion, the method adjusts the criteria controlling refinement to account for visibility and apparent size in the camera's view. Objectionable dynamic artifacts are avoided by anticipative refinement and smoothed coarsening. This approach preserves the appearance of detailed cloth throughout the animation while avoiding the wasted effort of simulating details that would not be discernible to the viewer. The computational savings realized by this method increase as scene complexity grows, producing a 2x speed-up for a single character and more than 4x for a small group.

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Browsing SCA 14: Eurographics/SIGGRAPH Symposium on Computer Animation by Subject "Computational Geometry and Object Modeling"

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