Results 1  10
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32
Adaptive Space Deformations Based on Rigid Cells
 COMPUT. GRAPH. FORUM
, 2007
"... We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical ..."
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Cited by 45 (7 self)
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We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical solver for the resulting nonlinear optimization problem. Scalability is achieved using an adaptive spatial discretization that is decoupled from the resolution of the embedded object. Our approach is versatile and easy to implement, supports thinshell and solid deformations of 2D and 3D objects, and is applicable to arbitrary samplebased representations, such as meshes, triangle soups, or point clouds.
Realtime Largedeformation Substructuring
"... This paper shows a method to extend 3D nonlinear elasticity model reduction to openloop multilevel reduced deformable structures. Given a volumetric mesh, we decompose the mesh into several subdomains, build a reduced deformable model for each domain, and connect the domains using inertia coupling ..."
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Cited by 23 (2 self)
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This paper shows a method to extend 3D nonlinear elasticity model reduction to openloop multilevel reduced deformable structures. Given a volumetric mesh, we decompose the mesh into several subdomains, build a reduced deformable model for each domain, and connect the domains using inertia coupling. This makes model reduction deformable simulations much more versatile: localized deformations can be supported without prohibitive computational costs, parts can be reused and precomputation times shortened. Our method does not use constraints, and can handle large domain rigid body motion in addition to large deformations, due to our derivation of the gradient and Hessian of the rotation matrix in polar decomposition. We show realtime examples with multilevel domain hierarchies and hundreds of reduced degrees of freedom.
A Generic and Scalable Pipeline for GPU Tetrahedral Grid Rendering
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics ha ..."
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Cited by 13 (1 self)
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Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics hardware architectures, large and deformable grids, as well as different rendering options. At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local barycentric coordinates. Then, sampling requires minimum GPU memory and texture access operations, and it maps efficiently onto a feedforward pipeline of multiple stages performing computation and geometry construction. We propose to spawn rendered elements from one single vertex. This makes the method amenable to upcoming Direct3D 10 graphics hardware which allows to create geometry on the GPU. By only modifying the algorithm slightly it can be used to render perpixel isosurfaces and to perform tetrahedral cell projection. As our method neither requires any preprocessing nor an intermediate grid representation it can efficiently deal with dynamic and large 3D meshes.
A realtime multigrid finite hexahedra method for elasticity simulation using CUDA. Simulation Modelling Practice and Theory 2011;19(2):801
"... We present a multigrid approach for simulating elastic deformable objects in real time on recent NVIDIA GPU architectures. To accurately simulate large deformations we consider the corotated strain formulation. Our method is based on a finite element discretization of the deformable object using he ..."
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Cited by 13 (1 self)
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We present a multigrid approach for simulating elastic deformable objects in real time on recent NVIDIA GPU architectures. To accurately simulate large deformations we consider the corotated strain formulation. Our method is based on a finite element discretization of the deformable object using hexahedra. It draws upon recent work on multigrid schemes for the efficient numerical solution of partial differential equations on such discretizations. Due to the regular shape of the numerical stencil induced by the hexahedral regime, and since we use matrixfree formulations of all multigrid steps, computations and data layout can be restructured to avoid execution divergence of parallel running threads and to enable coalescing of memory accesses into single memory transactions. This enables to effectively exploit the GPU’s parallel processing units and high memory bandwidth via the CUDA parallel programming API. We demonstrate performance gains of up to a factor of 27 and 4 compared to a highly optimized CPU implementation on a single CPU core and 8 CPU cores, respectively. For hexahedral models consisting of as many as 269,000 elements our approach achieves physicsbased simulation at 11 time steps per second. Keywords: Elasticity simulation, deformable objects, finite element methods, multigrid, GPU, CUDA
Quantum Monte Carlo on Graphical Processing Units
, 2007
"... Quantum Monte Carlo (QMC) is among the most accurate methods for solving the time independent Schrödinger equation. Unfortunately, the method is very expensive and requires a vast array of computing resources in order to obtain results of a reasonable convergence level. On the other hand, the method ..."
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Cited by 12 (0 self)
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Quantum Monte Carlo (QMC) is among the most accurate methods for solving the time independent Schrödinger equation. Unfortunately, the method is very expensive and requires a vast array of computing resources in order to obtain results of a reasonable convergence level. On the other hand, the method is not only easily parallelizable across CPU clusters, but as we report here, it also has a high degree of data parallelism. This facilitates the use of recent technological advances in Graphical Processing Units (GPUs), a powerful type of processor well known to computer gamers. In this paper we report on an endtoend QMC application with core elements of the algorithm running on a GPU. With individual kernels achieving as much as 30x speed up, the overall application performs at up to 6x relative to an optimized CPU implementation, yet requires only a modest increase in hardware cost. This demonstrates the speedup improvements possible for QMC in running on advanced hardware, thus exploring a path toward providing QMC level accuracy as a more standard tool. The major current challenge in running codes of this type on the GPU arises from the lack of fully compliant IEEE floating point implementations. To achieve better accuracy we propose the use of the Kahan summation formula in matrix multiplications. While this drops overall performance, we demonstrate that the proposed new algorithm can match CPU single precision.
Corotated Finite Elements Made Fast and Stable
, 2008
"... Multigrid finiteelement solvers using the corotational formulation of finite elements provide an attractive means for the simulation of deformable bodies exhibiting linear elastic response. The separation of rigid body motions from the total element motions using purely geometric methods or polar d ..."
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Cited by 12 (3 self)
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Multigrid finiteelement solvers using the corotational formulation of finite elements provide an attractive means for the simulation of deformable bodies exhibiting linear elastic response. The separation of rigid body motions from the total element motions using purely geometric methods or polar decomposition of the deformation gradient, however, can introduce instabilities for large element rotations and deformations. Furthermore, the integration of the corotational formulation into dynamic multigrid elasticity simulations requires to continually rebuild consistent system matrices at different resolution levels. The computational load imposed by these updates prohibits the use of large numbers of finite elements at rates comparable to the smallstrain finite element formulation. To overcome the first problem, we present a new method to extract the rigid body motion from total finite element displacements based on energy minimization. This results in a very stable corotational formulation that only slightly increases the computational overhead. We address the second problem by introducing a novel algorithm for computing sparse products of the form RKR T, as they have to be evaluated to update the multigrid hierarchy. By reformulating the problem into the simultaneous processing of a sequential data and control stream, cache miss penalties are significantly reduced. Even though the algorithm increases memory requirements, it accelerates the multigrid FE simulation by a factor of up to 4 compared to previous multigrid approaches. Due to the proposed improvements, finite element deformable body simulations using the corotational formulation can be performed at rates of 17 tps for up to 12k elements.
R.: A hexahedral multigrid approach for simulating cuts in deformable objects
 IEEE TVCG
"... Abstract—We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into ..."
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Cited by 11 (4 self)
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Abstract—We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions. Index Terms—Deformable objects, cutting, finite elements, multigrid, octree meshes. F 1
Robust tetrahedral meshing of triangle soups
 In Proc. Vision, Modeling, Visualization (VMV
, 2006
"... We propose a novel approach to generate coarse tetrahedral meshes which can be used in interactive simulation frameworks. The proposed algorithm processes unconstrained, i. e. unorientable and nonmanifold triangle soups. Since the volume bounded by an unconstrained surface is not defined, we tetrahe ..."
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Cited by 8 (4 self)
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We propose a novel approach to generate coarse tetrahedral meshes which can be used in interactive simulation frameworks. The proposed algorithm processes unconstrained, i. e. unorientable and nonmanifold triangle soups. Since the volume bounded by an unconstrained surface is not defined, we tetrahedralize the pseudo volume of the surface, namely the space that is intuitively occupied by the surface. Therefore, a new signed distance field approach is employed and a tetrahedral lattice is laid onto the distance field. Elements outside the pseudo volume are discarded and a smoothing filter is applied to the mesh boundary as a postprocessing step. Using our approach, we can generate coarse tetrahedral meshes from damaged surfaces and even triangle soups without any connectivity. Various examples underline the robustness of our approach. The usability of the resulting meshes is illustrated in the context of interactive deformable modeling. surface is a nontrivial task. Most mesh generators assume that the boundary surface is a closed and orientable manifold. However, many surfaces do not obey these criteria and the enclosed volume is not defined. Surfaces that are obtained by laser scans often contain holes and cracks (see Fig. 1), making it nonmanifold. Models that have been constructed using CAD software are composed of interpenetrating subparts (see Fig. 2). In theses cases, traditional volumization approaches have difficulties to determine the object volume which has to be tetrahedralized. Moreover, there exist object representations that are modeled from unconnected triangles (see Fig. 3). While a human observer can intuitively recognize the space occupied by this structure, a volumization approach fails to compute a plausible volumetric representation which hinders the generation of a tetrahedral mesh. 1
Freeform image
 Proceedings of Pacific Graphics
, 2007
"... In this paper we present a technique for image deformation in which the user is given flexible control over what kind of deformation to perform. Freeform image extends available image deformation techniques in that it provides a palette of intuitive tools including interactive object segmentation, s ..."
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Cited by 5 (0 self)
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In this paper we present a technique for image deformation in which the user is given flexible control over what kind of deformation to perform. Freeform image extends available image deformation techniques in that it provides a palette of intuitive tools including interactive object segmentation, stiffness editing and forcebased controls to achieve both a natural look and realistic animations of deforming parts. The model underlying our approach is physicsbased and it is amenable to a variety of different kinds of image manipulations ranging from asrigidaspossible to fully elastic deformations. We have developed a multigrid solver for quadrangular finite elements, which achieves realtime performance for high resolution pixel grids. On recent CPUs this solver can handle about 16K corotated finite elements at roughly 60 ms. 1. Introduction and Related
Manipulating, deforming and animating sampled object representations
 Computer Graphics Forum
, 2007
"... A sampled object representation (SOR) defines a graphical model using data obtained from a sampling process, which takes a collection of samples at discrete positions in space in order to capture certain geometrical and physical properties of one or more objects of interest. Examples of SORs include ..."
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Cited by 5 (1 self)
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A sampled object representation (SOR) defines a graphical model using data obtained from a sampling process, which takes a collection of samples at discrete positions in space in order to capture certain geometrical and physical properties of one or more objects of interest. Examples of SORs include images, videos, volume datasets and point datasets. Unlike many commonly used data representations in computer graphics, SORs lack in geometrical, topological and semantic information, which is much needed for controlling deformation and animation. Hence it poses a significant scientific and technical challenge to develop deformation and animation methods that operate upon SORs. Such methods can enable computer graphics and computer animation to benefit enormously from the advances of digital imaging technology. In this state of the art report, we survey a wide range of techniques that have been developed for manipulating, deforming and animating SORs. We consider a collection of elementary operations for manipulating SORs, which can serve as building blocks of deformation and animation techniques. We examine a collection of techniques that are designed to transform the geometry shape of deformable objects in sampled representations and pay particular attention to their deployment in surgical simulation. We review a collection of techniques for animating digital