Analytic Eigensystems for Isotropic Distortion Energies

Breannan Smith, Fernando de Goes, Theodore Kim

Many strategies exist for optimizing non-linear distortion energies in geometry and physics applications, but devising an approach that achieves the convergence promised by Newton-type methods remains challenging. In order to guarantee the positive semi-definiteness required by these methods, a numerical eigendecomposition or approximate regularization is usually needed. In this paper, we present analytic expressions for the eigensystems at each quadrature point of a wide range of isotropic distortion energies. These systems can then be used to project energy Hessians to positive semi-definiteness analytically. Unlike previous attempts, our formulation provides compact expressions that are valid both in 2D and 3D, and does not introduce spurious degeneracies. At its core, our approach utilizes the invariants of the stretch tensor that arises from the polar decomposition of the deformation gradient. We provide closed-form expressions for the eigensystems for all these invariants, and use them to systematically derive the eigensystems of any isotropic energy. Our results are suitable for geometry optimization over flat surfaces or volumes, and agnostic to both the choice of discretization and basis function. To demonstrate the efficiency of our approach, we include comparisons against existing methods on common graphics tasks such as surface parameterization and volume deformation.

Analytic Eigensystems for Isotropic Distortion Energies

Posted by christopherbatty on September 25th, 2018 | Comments Off on Analytic Eigensystems for Isotropic Distortion Energies Posted in Deformables

I-Cloth: Incremental Collision Handling for GPU-Based Interactive Cloth Simulation

Min Tang, Tongtong Wang, Zhongyuan Liu, Ruofeng Tong, and Dinesh Manocha

We present an incremental collision handling algorithm for GPU-based interactive cloth simulation. Our approach exploits the spatial and temporal coherence between successive iterations of an optimization-based solver for collision response computation. We present an incremental continuous collision detection algorithm that keeps track of deforming vertices and combine it with spatial hashing. We use a non-linear GPU-based impact zone solver to resolve the penetrations. We combine our collision handling algorithm with implicit integration to use large time steps. Our overall algorithm, I-Cloth, can simulate complex cloth deformation with a few hundred thousand vertices at 2-8 frames per second on a commodity GPU. We highlight its performance on different benchmarks and observe up to 7-10X speedup over prior algorithms.

I-Cloth: Incremental Collision Handling for GPU-Based Interactive Cloth Simulation

Posted by christopherbatty on September 25th, 2018 | Comments Off on I-Cloth: Incremental Collision Handling for GPU-Based Interactive Cloth Simulation Posted in Cloth, Collisions, Deformables

Decoupling Simulation Accuracy from Mesh Quality

Teseo Schneider, Yixin Hu, Jeremie Dumas, Xifeng Gao, Daniele Panozzo, Denis Zorin

For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p-refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs. Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance. Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary constraints or limitations of current meshing methods. By tackling mesh generation and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms.

Decoupling Simulation Accuracy from Mesh Quality

Posted by christopherbatty on September 25th, 2018 | Comments Off on Decoupling Simulation Accuracy from Mesh Quality Posted in Uncategorized

SIGGRAPH Asia 2018

Posted by christopherbatty on September 24th, 2018 | Comments Off on SIGGRAPH Asia 2018 Posted in Uncategorized

Editing Fluid Animation Using Flow Interpolation

Syuhei Sato, Yoshinori Dobashi, Tomoyuki Nishita

The computational cost for creating realistic fluid animations by numerical simulation is generally expensive. In digital production environments, existing precomputed fluid animations are often reused for different scenes in order to reduce the cost of creating scenes containing fluids. However, applying the same animation to different scenes often produces unacceptable results, so the animation needs to be edited. In order to help animators with the editing process, we develop a novel method for synthesizing the desired fluid animations by combining existing flow data. Our system allows the user to place flows at desired positions, and combine them. We do this by interpolating velocities at the boundaries between the flows. The interpolation is formulated as a minimization problem of an energy function, which is designed to take into account the inviscid, incompressible Navier-Stokes equations. Our method focuses on smoke simulations defined on a uniform grid. We demonstrate the potential of our method by showing a set of examples, including a large-scale sandstorm created from a few flow data simulated in a small-scale space.

Editing Fluid Animation Using Flow Interpolation

Posted by christopherbatty on September 20th, 2018 | Comments Off on Editing Fluid Animation Using Flow Interpolation Posted in Fluids

Hybrid Grains: Adaptive Coupling of Discrete and Continuum Simulations of Granular Media

Yonghao Yue*, Breannan Smith*, Peter Yichen Chen*, Maytee Chantharayukhonthorn*, Ken Kamrin, Eitan Grinspun

We propose a technique to simulate granular materials that exploits the dual strengths of discrete and continuum treatments. Discrete element simulations provide unmatched levels of detail and generality, but prove excessively costly when applied to large scale systems. Continuum approaches are computationally tractable, but limited in applicability due to built-in modeling assumptions; e.g., models suitable for granular flows typically fail to capture clogging, bouncing and ballistic motion. In our hybrid approach, an oracle dynamically partitions the domain into continuum regions where safe, and discrete regions where necessary. The domains overlap along transition zones, where a Lagrangian dynamics mass-splitting coupling principle enforces agreement between the two simulation states. Enrichment and homogenization operations allow the partitions to evolve over time. This approach accurately and efficiently simulates scenarios that previously required an entirely discrete treatment.

Hybrid Grains: Adaptive Coupling of Discrete and Continuum Simulations of Granular Media

Posted by christopherbatty on September 19th, 2018 | Comments Off on Hybrid Grains: Adaptive Coupling of Discrete and Continuum Simulations of Granular Media Posted in Deformables, Fluids, Rigid bodies

GPU Optimization of Material Point Methods

Ming Gao*, Xinlei Wang*, Kui Wu*, Andre Pradhana, Eftychios Sifakis, Cem Yuksel, Chenfanfu Jiang

The Material Point Method (MPM) has been shown to facilitate effective simulations of physically complex and topologically challenging materials, with a wealth of emerging applications in computational engineering and visual computing. Borne out of the extreme importance of regularity, MPM is given attractive parallelization opportunities on high-performance modern multiprocessors. Parallelization of MPM that fully leverages computing resources presents challenges that require exploring an extensive design-space for favorable data structures and algorithms. Unlike the conceptually simple CPU parallelization, where the coarse partition of tasks can be easily applied, it takes greater effort to reach the GPU hardware saturation due to its many-core SIMT architecture. In this paper we introduce methods for addressing the computational challenges of MPM and extending the capabilities of general simulation systems based on MPM, particularly concentrating on GPU optimization. In addition to our open-source high-performance framework, we also conduct performance analyses and benchmark experiments to compare against alternative design choices which may superficially appear to be reasonable, but can suffer from suboptimal performance in practice. Our explicit and fully implicit GPU MPM solvers are further equipped with a Moving Least Squares MPM heat solver and a novel sand constitutive model to enable fast simulations of a wide range of materials. We demonstrate that more than an order of magnitude performance improvement can be achieved with our GPU solvers. Practical high-resolution examples with up to ten million particles run in less than one minute per frame.

GPU Optimization of Material Point Methods

Posted by christopherbatty on September 19th, 2018 | Comments Off on GPU Optimization of Material Point Methods Posted in Deformables, Fluids

Physical Simulation of Environmentally Induced Thin Shell Deformation

Hsiao-yu Chen, Arnav Sastry, Wim M. van Rees, Etienne Vouga

We present a physically accurate low-order elastic shell model that incorporates active material response to dynamically changing stimuli such as heat, moisture, and growth. Our continuous formulation of the geometrically non-linear elastic energy derives from the principles of differential geometry, and as such naturally incorporates shell thickness, non-zero rest curvature, and physical material properties. By modeling the environmental stimulus as local, dynamic changes in the rest metric of the material, we are able to solve for the corresponding shape changes by integrating the equations of motions given this non-Euclidean rest state. We present models for differential growth and shrinking due to moisture and temperature gradients along and across the surface, and incorporate anisotropic growth by defining an intrinsic machine direction within the material. Comparisons with experiments and volumetric finite elements show that our simulations achieve excellent qualitative and quantitative agreement. By combining the reduced-order shell theory with appropriate physical models, our approach accurately captures all the physical phenomena while avoiding expensive volumetric discretization of the shell volume.

Physical Simulation of Environmentally Induced Thin Shell Deformation

Posted by christopherbatty on August 17th, 2018 | Comments Off on Physical Simulation of Environmentally Induced Thin Shell Deformation Posted in Shells

Mechanical Characterization of Structured Sheet Materials

Christian Schumacher, Steve Marschner, Markus Gross, Bernhard Thomaszewski

We propose a comprehensive approach to characterizing the mechanical properties of structured sheet materials, i.e., planar rod networks whose mechanics and aesthetics are inextricably linked. We establish a connection between the complex mesoscopic deformation behavior of such structures and their macroscopic elastic properties through numerical homogenization. Our approach leverages 3D Kirchhoff rod simulation in order to capture nonlinear effects for both in-plane and bending deformations. We apply our method to different families of structures based on isohedral tilings— a simple yet extensive and aesthetically interesting group of space-filling patterns. We show that these tilings admit a wide range of material properties, and our homogenization approach allows us to create concise and intuitive descriptions of a material’s direction-dependent macromechanical behavior that are easy to communicate even to non-experts. We perform this characterization for an extensive set of structures and organize these data in a material browser to enable efficient forward exploration of the aesthetic-mechanical space of structured sheet materials. We also propose an inverse design method to automatically find structure parameters that best approximate a user-specified target behavior.

Mechanical Characterization of Structured Sheet Materials

Posted by christopherbatty on August 9th, 2018 | Comments Off on Mechanical Characterization of Structured Sheet Materials Posted in Uncategorized

Methodology for Assessing Mesh-Based Contact Point Methods

Kenny Erleben

Computation of contact points is a critical sub-component of physics-based animation. The success and correctness of simulation results are very sensitive to the quality of the contact points. Hence, quality plays a critical role when comparing methods, and this is highly relevant for simulating objects with sharp edges. The importance of contact point quality is largely overlooked and lacks rigor and as such may become a bottleneck in moving the research field forward. We establish a taxonomy of contact point generation methods and lay down an analysis of what normal contact quality implies. The analysis enables us to establish a novel methodology for assessing and studying quality for mesh-based shapes. The core idea is based on a test suite of three complex cases and a small portfolio of simple cases. We apply our methodology to eight local contact point generation methods and conclude that the selected local methods are unable to provide correct information in all cases. The immediate benefit of the proposed methodology is a foundation for others to evaluate and select the best local method for their specific application. In the longer perspective, the presented work suggests future research focusing on semi-local methods.

Methodology for Assesing Mesh-Based Contact Point Methods

Posted by christopherbatty on August 9th, 2018 | Comments Off on Methodology for Assessing Mesh-Based Contact Point Methods Posted in Collisions, Deformables, Rigid bodies
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