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Divergence-Free Smoothed Particle Hydrodynamics
(ACM Siggraph, 2015) Bender, Jan; Koschier, Dan; Florence Bertails-Descoubes and Stelian Coros and Shinjiro Sueda
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.
Interactive Simulation of Rigid Body Dynamics in Computer Graphics
(The Eurographics Association and John Wiley and Sons Ltd., 2014) Bender, Jan; Erleben, Kenny; Trinkle, Jeff; Holly Rushmeier and Oliver Deussen
Interactive rigid body simulation is an important part of many modern computer tools, which no authoring tool nor game engine can do without. Such 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 have evolved and matured over the past 20 years. Furthermore, the paper communicates the mathematical and theoretical details in a pedagogical manner. This paper is not only a stake in the sand on what has been done, it also seeks to give the reader deeper insights to help guide their future research.
Simulating Inextensible Cloth Using Locking-free Triangle Meshes
(The Eurographics Association, 2011) Bender, Jan; Diziol, Raphael; Bayer, Daniel; Jan Bender and Kenny Erleben and Eric Galin
This paper presents an effcient method for the dynamic simulation of inextensible cloth. The triangle mesh for our cloth model is simulated using an impulse-based approach which is able to solve hard constraints. Using hard distance constraints on the edges of the triangle mesh removes too many degrees of freedom, resulting in a rigid motion. This is known as the locking problem which is typically solved by using rectangular meshes in existing impulse-based simulations. We solve this problem by using a nonconforming representation for the simulation model which unfortunately results in a discontinuous mesh. Therefore, we couple the original conforming mesh with the nonconforming elements and use it for collision handling and visualization.
Direct Position‐Based Solver for Stiff Rods
(© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Deul, Crispin; Kugelstadt, Tassilo; Weiler, Marcel; Bender, Jan; Chen, Min and Benes, Bedrich
In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the position‐based dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non‐linear equations using a non‐linear Gauss–Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver to solve the non‐linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well‐established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple 10 000 segments. In summary, our method allows the efficient simulation of stiff rods in the PBD framework with a speedup of two orders of magnitude compared to the original XPBD approach.We present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods. It is based on the XPBD algorithm, which extends Position‐Based Dynamics to simulate elastic objects with physically meaningful material parameters. However, the non‐linear Gauss‐Seidel solver of XPBD requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver which significantly improves convergence by solving all constraints of an acyclic structure simultaneously. We model rods using rigid segments connected by constraints. Bending and twisting constraints are derived from the Cosserat model. The high performance of our solver allows the simulation of rods consisting of multiple 10 000 segments with a speedup of two orders of magnitude compared to the original XPBD approach.
Efficient Self-Shadowing Using Image-Based Lighting on Glossy Surfaces
(The Eurographics Association, 2014) Knuth, Martin; Altenhofen, Christian; Kuijper, Arjan; Bender, Jan; Jan Bender and Arjan Kuijper and Tatiana von Landesberger and Holger Theisel and Philipp Urban
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 imagebased 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.
A Micropolar Material Model for Turbulent SPH Fluids
(ACM, 2017) Bender, Jan; Koschier, Dan; Kugelstadt, Tassilo; Weiler, Marcel; Bernhard Thomaszewski and KangKang Yin and Rahul Narain
In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). As already investigated in previous works, SPH fluid simulations su er from numerical di usion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier- Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids also have a field of microrotation which represents existing vortices and provides a source for new ones. However, classical micropolar materials are viscous and the translational and the rotational motion are coupled in a dissipative way. Since our goal is to simulate turbulent fluids, we introduce a novel modi ed micropolar material for inviscid fluids with a non-dissipative coupling Our model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible.
Level of Detail for Real-Time Volumetric Terrain Rendering
(The Eurographics Association, 2013) Scholz, Manuel; Bender, Jan; Dachsbacher, Carsten; Michael Bronstein and Jean Favre and Kai Hormann
Terrain rendering is an important component of many GIS applications and simulators. Most methods rely on heightmap-based terrain which is simple to acquire and handle, but has limited capabilities for modeling features like caves, steep cliffs, or overhangs. In contrast, volumetric terrain models, e.g. based on isosurfaces can represent arbitrary topology. In this paper, we present a fast, practical and GPU-friendly level of detail algorithm for large scale volumetric terrain that is specifically designed for real-time rendering applications. Our algorithm is based on a longest edge bisection (LEB) scheme. The resulting tetrahedral cells are subdivided into four hexahedra, which form the domain for a subsequent isosurface extraction step. The algorithm can be used with arbitrary volumetric models such as signed distance fields, which can be generated from triangle meshes or discrete volume data sets. In contrast to previous methods our algorithm does not require any stitching between detail levels. It generates crack free surfaces with a good triangle quality. Furthermore, we efficiently extract the geometry at runtime and require no preprocessing, which allows us to render infinite procedural content with low memory consumption.
Hierarchical hp-Adaptive Signed Distance Fields
(The Eurographics Association, 2016) Koschier, Dan; Deul, Crispin; Bender, Jan; Ladislav Kavan and Chris Wojtan
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.
A Physically Consistent Implicit Viscosity Solver for SPH Fluids
(The Eurographics Association and John Wiley & Sons Ltd., 2018) Weiler, Marcel; Koschier, Dan; Brand, Magnus; Bender, Jan; Gutierrez, Diego and Sheffer, Alla
In this paper, we present a novel physically consistent implicit solver for the simulation of highly viscous fluids using the Smoothed Particle Hydrodynamics (SPH) formalism. Our method is the result of a theoretical and practical in-depth analysis of the most recent implicit SPH solvers for viscous materials. Based on our findings, we developed a list of requirements that are vital to produce a realistic motion of a viscous fluid. These essential requirements include momentum conservation, a physically meaningful behavior under temporal and spatial refinement, the absence of ghost forces induced by spurious viscosities and the ability to reproduce complex physical effects that can be observed in nature. On the basis of several theoretical analyses, quantitative academic comparisons and complex visual experiments we show that none of the recent approaches is able to satisfy all requirements. In contrast, our proposed method meets all demands and therefore produces realistic animations in highly complex scenarios. We demonstrate that our solver outperforms former approaches in terms of physical accuracy and memory consumption while it is comparable in terms of computational performance. In addition to the implicit viscosity solver, we present a method to simulate melting objects. Therefore, we generalize the viscosity model to a spatially varying viscosity field and provide an SPH discretization of the heat equation.
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.

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