Marcel Weiler, Dan Koschier and Jan Bender, Projective Fluids, In Proceedings of ACM SIGGRAPH Motion in Games, 2016

 

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Abstract

We present a new method for particle based fluid simulation, using a combination of Projective Dynamics and Smoothed Particle Hydrodynamics (SPH). The Projective Dynamics framework allows the fast simulation of a wide range of constraints. It offers great stability through its implicit time integration scheme and is parallelizable in large parts, so that it can make use of modern multi core CPUs. Yet existing work only uses Projective Dynamics to simulate various kinds of soft bodies and cloth. We are the first ones to incorporate fluid simulation into the Projective Dynamics framework. Our proposed fluid constraints are derived from SPH and seamlessly integrate into the existing method. Furthermore, we adapt the solver to handle the constantly changing constraints that appear in fluid simulation. We employ a highly parallel matrix-free conjugate gradient solver, and thus do not require expensive matrix factorizations.


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Matthias Müller, Jan Bender, Nuttapong Chentanez and Miles Macklin, A Robust Method to Extract the Rotational Part of Deformations, In Proceedings of ACM SIGGRAPH Motion in Games, 2016

 

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Abstract

We present a novel algorithm to extract the rotational part of an arbitrary 3x3 matrix. This problem lies at the core of two popular simulation methods in computer graphics, the co-rotational Finite Element Method and Shape Matching techniques. In contrast to the traditional method based on polar decomposition, degenerate configurations and inversions are handled robustly and do not have to be treated in a special way. In addition, our method can be implemented with only a few lines of code without branches which makes it particularly well suited for GPU-based applications. We demonstrate the robustness, coherence and efficiency of our method by comparing it to stabilized polar decomposition in several simulation scenarios.


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Jan Bender and Dan Koschier, Divergence-Free SPH for Incompressible and Viscous Fluids, IEEE Transactions on Visualization and Computer Graphics, 2016

 

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Abstract

In this paper we present a novel Smoothed Particle Hydrodynamics (SPH) method for the efficient and stable simulation of incompressible fluids. The most efficient SPH-based approaches enforce incompressibility either on position or velocity level. However, the continuity equation for incompressible flow demands to maintain a constant density and a divergence-free velocity field. We propose a combination of two novel implicit pressure solvers enforcing both a low volume compression as well as a divergence-free velocity field. While a compression-free fluid is essential for realistic physical behavior, a divergence-free velocity field drastically reduces the number of required solver iterations and increases the stability of the simulation significantly. Thanks to the improved stability, our method can handle larger time steps than previous approaches. This results in a substantial performance gain since the computationally expensive neighborhood search has to be performed less frequently. Moreover, we introduce a third optional implicit solver to simulate highly viscous fluids which seamlessly integrates into our solver framework. Our implicit viscosity solver produces realistic results while introducing almost no numerical damping. We demonstrate the efficiency, robustness and scalability of our method in a variety of complex simulations including scenarios with millions of turbulent particles or highly viscous materials.


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Dan Koschier, Crispin Deul and Jan Bender, Hierarchical hp-Adaptive Signed Distance Fields, In Proceedings of ACM SIGGRAPH / EUROGRAPHICS Symposium on Computer Animation (SCA), 2016

 

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Abstract

In this paper we propose a novel method to construct hierarchical $hp$-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell's polynomial degree (p) in order to construct a very accurate but memory-efficient representation. Presenting a novel criterion to decide whether to apply h- or p-refinement, we demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption than previous approaches. Finally, we demonstrate the usage of our representation as collision detector for geometrically highly complex solid objects in the application area of physically-based simulation.


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Jan Bender and Dan Koschier, Divergence-Free Smoothed Particle Hydrodynamics, In Proceedings of ACM SIGGRAPH / EUROGRAPHICS Symposium on Computer Animation (SCA), 2015

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Abstract

In this paper we introduce an efficient and stable implicit SPH method for the physically-based simulation of incompressible fluids. In the area of computer graphics the most efficient SPH approaches focus solely on the correction of the density error to prevent volume compression. However, the continuity equation for incompressible flow also demands a divergence-free velocity field which is neglected by most methods. Although a few methods consider velocity divergence, they are either slow or have a perceivable density fluctuation.

Our novel method uses an efficient combination of two pressure solvers which enforce low volume compression (below 0.01%) and a divergence-free velocity field. This can be seen as enforcing incompressibility both on position level and velocity level. The first part is essential for realistic physical behavior while the divergence-free state increases the stability significantly and reduces the number of solver iterations. Moreover, it allows larger time steps which yields a considerable performance gain since particle neighborhoods have to be updated less frequently. Therefore, our divergence-free SPH (DFSPH) approach is significantly faster and more stable than current state-of-the-art SPH methods for incompressible fluids. We demonstrate this in simulations with millions of fast moving particles.


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Jan Bender, Matthias Müller and Miles Macklin, Position-Based Simulation Methods in Computer Graphics, In Tutorial Proceedings of Eurographics, 2015

Course Notes   BibTex   Source Code


Abstract

The physically-based simulation of mechanical effects has been an important research topic in computer graphics for more than two decades. Classical methods in this field discretize Newton's second law and determine different forces to simulate various effects like stretching, shearing, and bending of deformable bodies or pressure and viscosity of fluids, to mention just a few. Given these forces, velocities and finally positions are determined by a numerical integration of the resulting accelerations.

In the last years position-based simulation methods have become popular in the graphics community. In contrast to classical simulation approaches these methods compute the position changes in each simulation step directly, based on the solution of a quasi-static problem. Therefore, position-based approaches are fast, stable and controllable which make them well-suited for use in interactive environments. However, these methods are generally not as accurate as force-based methods but still provide visual plausibility. Hence, the main application areas of position-based simulation are virtual reality, computer games and special effects in movies and commercials.

In this tutorial we first introduce the basic concept of position-based dynamics. Then we present different solvers and compare them with the classical implicit Euler method. We discuss approaches to improve the convergence of these solvers. Moreover, we show how position-based methods are applied to simulate hair, cloth, volumetric deformable bodies, rigid body systems and fluids. We also demonstrate how complex effects like anisotropy or plasticity can be simulated and introduce approaches to improve the performance. Finally, we give an outlook and discuss open problems.


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Cloth

Armadillos

Elastoplastic Dragon

Elastoplastic Dragon

Millipede

Millipede

Pile

Pile

Different constraints

Different constraints


Jan Bender, Dan Koschier, Patrick Charrier and Daniel Weber, Position-Based Simulation of Continuous Materials, Computers & Graphics 44, 2014

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Abstract

We introduce a novel fast and robust simulation method for deformable solids that supports complex physical effects like lateral contraction, anisotropy or elastoplasticity. Our method uses a continuum-based formulation to compute strain and bending energies for two- and three-dimensional bodies. In contrast to previous work, we do not determine forces to reduce these potential energies, instead we use a position-based approach. This combination of a continuum-based formulation with a position-based method enables us to keep the simulation algorithm stable, fast and controllable while providing the ability to simulate complex physical phenomena lacking in former position-based approaches. We demonstrate how to simulate cloth and volumetric bodies with lateral contraction, bending, plasticity as well as anisotropy and proof robustness even in case of degenerate or inverted elements. Due to the continuous material model of our method further physical phenomena like fracture or viscoelasticity can be easily implemented using already existing approaches. Furthermore, a combination with other geometrically motivated methods is possible.


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Armadillos
Cloth

Dan Koschier, Sebastian Lipponer and Jan Bender, Adaptive Tetrahedral Meshes for Brittle Fracture Simulation, In Proceedings of ACM SIGGRAPH / EUROGRAPHICS Symposium on Computer Animation (SCA), 2014, accepted

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Abstract

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.


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Wall
Wall
Armadillo
Tori

Crispin Deul, Patrick Charrier and Jan Bender, Position-Based Rigid Body Dynamics, In Proceedings of the 27th International Conference on Computer Animation and Social Agents, 2014

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Abstract

We propose a position-based approach for large-scale simulations of rigid bodies at interactive frame-rates. Our method solves positional constraints between rigid bodies and therefore integrates nicely with other position-based methods. Interaction of particles and rigid bodies through common constraints enables two-way coupling with deformables. The method exhibits exceptional performance and stability while being user-controllable and easy to implement. Various results demonstrate the practicability of our method for the resolution of collisions, contacts, stacking and joint constraints.


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Mobile
Cloth model
Collision model
Elk test

Jan Bender, Dynamiksimulation in der Computergraphik, Habilitationsschrift, KIT, KIT Scientific Publishing, 2014

 

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Abstract

Die physikalisch-basierte Simulation von Starrkörpern und deformierbaren Festkörpern ist ein wichtiges und aktuelles Forschungsgebiet in der Computergraphik und ein essentieller Bestandteil in vielen Anwendungen, wie z.B. Virtual Prototyping, Computeranimationen, Spiele, Spezialeffekte in Filmen oder Trainingssimulatoren. Dabei stehen oft interaktive Simulationen im Vordergrund, in denen ein Benutzer in Echtzeit mit den simulierten Körpern interagieren kann. Dadurch werden hohe Anforderungen an die Geschwindigkeit und Stabilität der Simulationsverfahren gestellt.

In dieser Arbeit werden interaktive Simulationsmethoden für Mehrkörpersysteme, Textilien und inkompressible deformierbare Volumenkörper vorgestellt. Außerdem wird gezeigt, wie die Simulation durch den Einsatz GPU-basierter Methoden deutlich beschleunigt werden kann.


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Terrain1
Terrain2
Terrain3
Terrain4

Jan Bender, Matthias Müller, Miguel A. Otaduy, Matthias Teschner and Miles Macklin, A Survey on Position-Based Simulation Methods in Computer Graphics, Computer Graphics Forum 33, 6, 2014

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Abstract

The dynamic simulation of mechanical effects has a long history in computer graphics. The classical methods in this field discretize Newton's second law in a variety of Lagrangian or Eulerian ways, and formulate forces appropriate for each mechanical effect: joints for rigid bodies; stretching, shearing, or bending for deformable bodies; and pressure, or viscosity for fluids, to mention just a few. In the last years the class of position-based methods has become popular in the graphics community. These kinds of methods are fast, stable and controllable which make them well-suited for use in interactive environments. Position-based methods are not as accurate as force-based methods in general but they provide visual plausibility. Therefore, the main application areas of these approaches are virtual reality, computer games and special effects in movies.

This state-of-the-art report covers the large variety of position-based methods that were developed in the field of physically-based simulation. We will introduce the concept of position-based dynamics, present dynamic simulation based on shape matching and discuss data-driven upsampling approaches. Furthermore, we will present several applications for these methods.


Images

Cloth

Cloth

Wrinkle Mesh

Wrinkle Mesh

Armadillos

Armadillos

Ducks and tori

Ducks and tori

hair

Hair simulation


Crispin Deul and Jan Bender, Physically-Based Character Skinning, Virtual Reality Interactions and Physical Simulations (VRIPhys), 2013

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Abstract

In this paper we present a novel multi-layer model for physically-based character skinning. In contrast to geometric approaches which are commonly used in the field of character skinning, physically-based methods can simulate secondary motion effects. Furthermore, these methods can handle collisions and preserve the volume of the model without the need of an additional post-process. Physically-based approaches are computationally more expensive than geometric methods but they provide more realistic results. Recent works in this area use finite element simulations to model the elastic behavior of skin. These methods require the generation of a volumetric mesh for the skin shape in a pre-processing step. It is not easy for an artist to model the different elastic behaviors of muscles, fat and skin using a volumetric mesh since there is no clear assignment between volume elements and tissue types. For our novel multi-layer model the mesh generation is very simple and can be performed automatically. Furthermore, the model contains a layer for each kind of tissue. Therefore, the artist can easily control the elastic behavior by adjusting the stiffness parameters for muscles, fat and skin. We use shape matching with oriented particles and a fast summation technique to simulate the elastic behavior of our skin model and a position-based constraint enforcement to handle collisions, volume conservation and the coupling of the skeleton with the deformable model. Position-based methods have the advantage that they are fast, unconditionally stable, controllable and provide visually plausible results.


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Woody1small linear blend skinning
Woody2small our approach

Jan Bender, Kenny Erleben, Jeff Trinkle and Erwin Coumans, Interactive Simulation of Rigid Body Dynamics in Computer Graphics, In STAR Proceedings of Eurographics, 2012

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Abstract

Interactive rigid body simulation is an important part of many modern computer tools. No authoring tool nor a game engine can do without. The high performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems.

This paper is a self contained state-of-the-art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which has evolved and matured over the past 20 years. The paper covers applications and the usage of interactive rigid body simulation.

Besides the mathematical and theoretical details that this paper communicates in a pedagogical manner the paper surveys common practice and reflects on applications of interactive rigid body simulation. The grand merger of interactive and off-line simulation methods is imminent, multi-core is everyman's property. These observations pose future challenges for research which we reflect on. In perspective several avenues for possible future work is touched upon such as more descriptive models and contact point generation problems. This paper is not only a stake in the sand on what has been done, it also seeks to give newcomers practical hands on advices and reflections that can give experienced researchers afterthought for the future.

CrashTest

Crash test

OfficeToy

Newton's cradle

roof_on_impact

Roof on impact

generalconvex_jinngine_3012

Jinngine

temple_260k

Temple

silo_1

Silo


Nikolas Schmitt, Martin Knuth, Jan Bender and Arjan Kuijper, Multilevel Cloth Simulation using GPU Surface Sampling, Virtual Reality Interactions and Physical Simulations (VRIPhys), 2013

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Abstract

Today most cloth simulation systems use triangular mesh models. However, regular grids allow many optimizations as connectivity is implicit, warp and weft directions of the cloth are aligned to grid edges and distances between particles are equal. In this paper we introduce a cloth simulation that combines both model types. All operations that are performed on the CPU use a low-resolution triangle mesh while GPU-based methods are performed efficiently on a high-resolution grid representation. Both models are coupled by a sampling operation which renders triangle vertex data into a texture and by a corresponding projection of texel data onto a mesh. The presented scheme is very flexible and allows individual components to be performed on different architectures, data representations and detail levels. The results are combined using shader programs which causes a negligible overhead. We have implemented CPU-based collision handling and a GPU-based hierarchical constraint solver to simulate systems with more than 230k particles in real-time.


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Cloth
Cloth
Cloth