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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Martin Knuth, Jan Bender, Michael Goesele and Arjan Kuijper, Deferred Warping, In IEEE Computer Graphics and Applications, 2016

 

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Abstract

We introduce deferred warping, a novel approach for real-time deformation of 3D objects attached to an animated or manipulated surface. Our target application is virtual prototyping of garments where 2D pattern modeling is combined with 3D garment simulation which allows an immediate validation of the design. The technique works in two steps: First, the surface deformation of the target object is determined and the resulting transformation field is stored as a matrix texture. Then the matrix texture is used as look-up table to transform a given geometry onto a deformed surface. Splitting the process in two steps yields a large flexibility since different attachment types can be realized by simply defining specific mapping functions. Our technique can directly handle complex topology changes within the surface. We demonstrate a fast implementation in the vertex shading stage allowing the use of highly decorated surfaces with millions of triangles in real-time.


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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.


Images

Cloth

Armadillos

Elastoplastic Dragon

Elastoplastic Dragon

Millipede

Millipede

Pile

Pile

Different constraints

Different constraints


Martin Knuth, Christian Altenhofen, Arjan Kuijper and Jan Bender, Efficient Self-Shadowing Using Image-Based Lighting on Glossy Surfaces, In Proceedings of Vision, Modeling and Visualization, 2014

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Abstract

In this paper we present a novel natural illumination approach for real-time rasterization-based rendering with environment map-based high dynamic range lighting. Our approach allows to use all kinds of glossiness values for surfaces, ranging continuously from completely diffuse up to mirror-like glossiness. This is achieved by combining cosine-based diffuse, glossy and mirror reflection models in one single lighting model. We approximate this model by filter functions, which are applied to the environment map. This results in a fast, image-based lookup for the different glossiness values which gives our technique the high performance that is necessary for real-time rendering. In contrast to existing real-time rasterization-based natural illumination techniques, our method has the capability of handling high gloss surfaces with directional self-occlusion. While previous works exchange the environment map by virtual point light sources in the whole lighting and shadow computation, we keep the full image information of the environment map in the lighting process and only use virtual point light sources for the shadow computation. Our technique was developed for the usage in real-time virtual prototyping systems for garments since here typically a small scene is lit by a large environment which fulfills the requirements for image-based lighting. In this application area high performance rendering techniques for dynamic scenes are essential since a physical simulation is usually running in parallel on the same machine. However, also other applications can benefit from our approach.


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Cloth
Dragon
Dragon
Teapot

Manuel Scholz, Jan Bender and Carsten Dachsbacher, Real-Time Isosurface Extraction with View-Dependent Level of Detail and Applications, Computer Graphics Forum 34, 1, 2015

 

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Abstract

Volumetric scalar datasets are common in many scientific, engineering, and medical applications where they originate from measurements or simulations. Furthermore, they can represent geometric scene content, e.g. as distance or density fields. Often isosurfaces are extracted, either for indirect volume visualization in the former category, or to simply obtain a polygonal representation in case of the latter. However, even moderately sized volume datasets can result in complex isosurfaces which are challenging to recompute in real-time, e.g. when the user modifies the isovalue or when the data itself is dynamic. In this paper, we present a GPU-friendly algorithm for the extraction of isosurfaces, which provides adaptive level of detail rendering with view-dependent tessellation. It is based on a longest edge bisection scheme where the resulting tetrahedral cells are subdivided into four hexahedra, which then form the domain for the subsequent isosurface extraction step. Our algorithm generates meshes with good triangle quality even for highly nonlinear scalar data. In contrast to previous methods, it does not require any stitching between regions of different levels of detail. As all computation is performed at run-time and no preprocessing is required, the algorithm naturally supports dynamic data and allows us to change isovalues at any time.


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teaser

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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Images

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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Images

Wall
Wall
Armadillo
Tori

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

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, 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