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

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Abstract

We 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.


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Bridge

Bridge

Cloth

Cloth

Armadillo

Armadillo

Pensatore

Pensatore

 


Jan Bender, Daniel Weber and Raphael Diziol, Fast and stable cloth simulation based on multi-resolution shape matching, Computers & Graphics 37, 8, 2013

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Abstract

We present an efficient and unconditionally stable method which allows the deformation of very complex stiff cloth models in real-time. This method is based on a shape matching approach which uses edges and triangles as 1D and 2D regions to simulate stretching and shearing resistance. Previous shape matching approaches require large overlapping regions to simulate stiff materials. This unfortunately also affects the bending behavior of the model. Instead of using large regions, we introduce a novel multi-resolution shape matching approach to increase only the stretching and shearing stiffness. Shape matching is performed for each level of the multi-resolution model and the results are propagated from one level to the next one. To preserve the fine wrinkles of the cloth on coarse levels of the hierarchy we present a modified version of the original shape matching method. The introduced method for cloth simulation can perform simulations in linear time and has no numerical damping. Furthermore, we show that multi-resolution shape matching can be performed efficiently on the GPU.


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Woody1small
Woody2small
Dragon3
Dragon4

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

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)

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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).


Abstract

We 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.


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Armadillos

Armadillos

Balls

Balls

Ducks and tori

Ducks and tori

Volume loss comparison

Volume loss comparison

Inverted Armadillo

Inverted Armadillo

Twirl

Twirl

Comparison with FastLSM

Comparison with FastLSM

Velocity correction

Velocity correction