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Daniel Weber, Jan Bender, Markus Schnoes, Andre Stork and Dieter Fellner, Efficient GPU data structures and methods to solve sparse linear systems in dynamics applications, In Computer Graphics Forum, Computer Graphics Forum 32, 1, 2013 PDF BibTex AbstractWe present graphics processing unit (GPU) data structures and algorithms to efficiently solve sparse linear systems that are typically required in simulations of multi-body systems and deformable bodies. Thereby, we introduce an efficient sparse matrix data structure that can handle arbitrary sparsity patterns and outperforms current state-of-the-art implementations for sparse matrix vector multiplication. Moreover, an efficient method to construct global matrices on the GPU is presented where hundreds of thousands of individual element contributions are assembled in a few milliseconds. A finite-element-based method for the simulation of deformable solids as well as an impulse-based method for rigid bodies are introduced in order to demonstrate the advantages of the novel data structures and algorithms. These applications share the characteristic that a major computational effort consists of building and solving systems of linear equations in every time step. Our solving method results in a speed-up factor of up to 13 in comparison to other GPU methods. Video Images
 Raphael Diziol, Jan Bender and Daniel Bayer, Robust Real-Time Deformation of Incompressible Surface Meshes, In Proceedings of ACM SIGGRAPH / EUROGRAPHICS Symposium on Computer Animation (SCA), 2011, Best paper award (Honorable Mention) PDF BibTex ACM, (2011) This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definite version will be published in Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (2011). AbstractWe introduce an efficient technique for robustly simulating incompressible objects with thousands of elements in real-time. Instead of considering a tetrahedral model, commonly used to simulate volumetric bodies, we simply use their surfaces. Not requiring hundreds or even thousands of elements in the interior of the object enables us to simulate more elements on the surface, resulting in high quality deformations at low computation costs. The elasticity of the objects is robustly simulated with a geometrically motivated shape matching approach which is extended by a fast summation technique for arbitrary triangle meshes suitable for an efficient parallel computation on the GPU. Moreover, we present an oscillation-free and collision-aware volume constraint, purely based on the surface of the incompressible body. The novel heuristic we propose in our approach enables us to conserve the volume, both globally and locally. Our volume constraint is not limited to the shape matching method and can be used with any method simulating the elasticity of an object. We present several examples which demonstrate high quality volume conserving deformations and compare the run-times of our CPU implementation, as well as our GPU implementation with similar methods. Video Images
Raphael Diziol, Daniel Bayer and Jan Bender, Simulating Almost Incompressible Deformable Objects, Virtual Reality Interactions and Physical Simulations (VRIPhys), Karlsruhe, November 5-6, 2009 PDF BibTexAbstractWe present a new method for simulating almost incompressible deformable objects. A tetrahedral model is used to represent and restore the volume during the simulation. The new constraint computes impulses in the onering of each vertex of the tetrahedral model, in order to conserve the initial volume. With different parameters, the presented method can handle a large variety of different deformation behaviors, ranging from stiff to large deformations and even plastic deformations. The algorithm is easy to implement and reduces the volume error to less than 1% in most situations, even when large deformations are applied.
Raphael Diziol, Jan Bender and Daniel Bayer, Volume Conserving Simulation of Deformable Bodies, Short Paper Proceedings of Eurographics, Munich, March 2009 PDF BibTexAbstractWe present a new method for simulating volume conserving deformable bodies using an impulse-based approach. In order to simulate a deformable body a tetrahedral model is generated from an arbitrary triangle mesh. All resulting tetrahedrons are assigned to volume constraints which ensure the conservation of the total volume. For the simulation of such a constraint impulses are computed and applied to the particles of the assigned tetrahedrons. The algorithm is easy to implement and ensures exact volume conservation in each simulation step.
Jan Bender and Daniel Bayer, "Parallel simulation of inextensible cloth", Virtual Reality Interactions and Physical Simulations (VRIPhys), Grenoble, November 13-14, 2008 PDF BibTexAbstractThis paper presents an efficient simulation method for parallel cloth simulation. The presented method uses an impulse-based approach for the simulation. Cloth simulation has many application areas like computer animation, computer games or virtual reality. Simulation methods often make the assumption that cloth is an elastic material. In this way the simulation can be performed very efficiently by using spring forces. These methods disregard the fact that many textiles cannot be stretched significantly. The simulation of inextensible textiles with methods based on spring forces leads to stiff differential equations which cause a loss of performance. In contrast to that, in this paper a method is presented that simulates cloth by using impulses. The mesh of a cloth model is subdivided into strips of constraints. The impulses for each strip can be computed in linear time. The strips that have no common particle are independent from each other and can be solved in parallel. The impulse-based method allows the realistic simulation of inextensible textiles in real-time. Jan Bender, "Impulse-based simulation of inextensible cloth", Computer Graphics and Visualization (CGV 2008) - IADIS Multi Conference on Computer Science and Information Systems, Amsterdam 2008 PDF BibTexAbstractIn this paper an impulse-based method for cloth simulation is presented. The simulation of cloth is required in different application areas like computer animation, virtual reality or computer games. Simulation methods often assume that cloth is an elastic material. With this assumption the simulation can be performed very efficiently using spring forces. The problem is that many textiles cannot be stretched significantly. A realistic simulation of these textiles with spring forces leads to stiff differential equations which cause a deterioration of performance. The impulse-based method described in this paper solves this problem and allows the realistic simulation of inelastic textiles. Jan Bender, Impulse-based dynamic simulation in linear time, In Journal of Computer Animation and Virtual Worlds, John Wiley & Sons Ltd, 2007 PDF BibTex Abstract:This paper describes an impulse-based dynamic simulation method for articulated bodies which has a linear time complexity. Existing linear-time methods are either based on a reduced-coordinate formulation or on Lagrange multipliers. The impulse-based simulation has advantages over these well-known methods. Unlike reduced-coordinate methods, it handles nonholonomic constraints like velocity-dependent ones and is very easy to implement. In contrast to Lagrange multiplier methods the impulse-based approach has no drift problem and an additional stabilisation is not necessary. The presented method computes a simulation step in O(n) time for acyclic multi-body systems containing equality constraints. Closed kinematic chains can be handled by dividing the model into different acyclic parts. Each of these parts is solved independently from each other. The dependencies between the single parts are solved by an iterative method. In the same way inequality constraints can be integrated in the simulation process in order to handle collisions and permanent contacts with dynamic and static friction. Additional information:The paper describes an algorithm to compute the required impulses in linear time and linear space. Jan Bender and Alfred Schmitt, Fast Dynamic Simulation of Multi-Body Systems Using Impulses, Virtual Reality Interactions and Physical Simulations (VRIPhys), 2006  PDF BibTex Abstract:
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Jan Bender and Alfred Schmitt, Constraint-based collision and contact handling using impulses, In Proceedings of the 19th international conference on computer animation & social agents, 2006 PDF BibTex Abstract:
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