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    Vega: Non-Linear FEM Deformable Object Simulator
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Sin, F. S.; Schroeder, D.; Barbic, J.; Holly Rushmeier and Oliver Deussen
    This practice and experience paper describes a robust C++ implementation of several non-linear solid three-dimensional deformable object strategies commonly employed in computer graphics, named the Vega finite element method (FEM) simulation library. Deformable models supported include co-rotational linear FEM elasticity, Saint-Venant Kirchhoff FEM model, mass-spring system and invertible FEM models: neo-Hookean, Saint-Venant Kirchhoff and Mooney-Rivlin. We provide several timestepping schemes, including implicit Newmark and backward Euler integrators, and explicit central differences. The implementation of material models is separated from integration, which makes it possible to employ our code not only for simulation, but also for deformable object control and shape modelling. We extensively compare the different material models and timestepping schemes. We provide practical experience and insight gained while using our code in several computer animation and simulation research projects.This practice and experience paper describes a robust C++ implementation of several nonlinear solid 3D deformable object strategies commonly employed in computer graphics, named the Vega FEM simulation library. Deformable models supported include co-rotational linear FEM elasticity, Saint-Venant Kirchhoff FEM model, mass-spring system, and invertible FEM models: neo-Hookean, Saint-Venant Kirchhoff, and Mooney-Rivlin. We provide several timestepping schemes, including implicit Newmark and backward Euler integrators, and explicit central differences. The implementation of material models is separated from integration, which makes it possible to employ our code not only for simulation, but also for deformable object control and shape modeling. We extensively compare the different material models and timestepping schemes. We provide practical experience and insight gained while using our code in several computer animation and simulation research projects.
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    Synthetic Controllable Turbulence Using Robust Second Vorticity Confinement
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) He, S.; Lau, R. W. H.; Holly Rushmeier and Oliver Deussen
    Capturing fine details of turbulence on a coarse grid is one of the main tasks in real-time fluid simulation. Existing methods for doing this have various limitations. In this paper, we propose a new turbulence method that uses a refined second vorticity confinement method, referred to as robust second vorticity confinement, and a synthesis scheme to create highly turbulent effects from coarse grid. The new technique is sufficiently stable to efficiently produce highly turbulent flows, while allowing intuitive control of vortical structures. Second vorticity confinement captures and defines the vortical features of turbulence on a coarse grid. However, due to the stability problem, it cannot be used to produce highly turbulent flows. In this work, we propose a robust formulation to improve the stability problem by making the positive diffusion term to vary with helicity adaptively. In addition, we also employ our new method to procedurally synthesize the high-resolution flow fields. As shown in our results, this approach produces stable high-resolution turbulence very efficiently.Capturing fine details of turbulence on a coarse grid is one of the main tasks in real-time fluid simulation. Existing methods for doing this have various limitations. In this paper, we propose a new turbulence method that uses a refined Second Vorticity Confinement method, referred to as Robust Second Vorticity Confinement, and a synthesis scheme to create highly turbulent effects from coarse grid. The new technique is sufficiently stable to efficiently produce highly turbulent flows, while allowing intuitive control of vortical structures. Second Vorticity Confinement captures and defines the vortical features of turbulence on a coarse grid. However, due to the stability problem, it cannot be used to produce highly turbulent flows. In this work, we propose a robust formulation to improve the stability problem by making the positive diffusion term to vary with helicity adaptively. In addition, we also employ our new method to procedurally synthesize the high resolution flow fields. As shown in our results, this approach produces stable high resolution turbulence very efficiently.
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    Interactive Planarization and Optimization of 3D Meshes
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Poranne, Roi; Ovreiu, Elena; Gotsman, Craig; Holly Rushmeier and Oliver Deussen
    Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshesâ ''those having planar facesâ ''are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least-squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints.Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes - those having planar faces - are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing and editing polyhedral meshes. Efficiency is achieved thanks to a numerical procedure combining an alternating least-squares approach with the penalty method. This approach is generalized to manipulate other subsets of polyhedral meshes, as defined by a variety of other constraints.
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    Perceptual Metrics for Static and Dynamic Triangle Meshes
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Corsini, M.; Larabi, M. C.; Lavoué, G.; Petřík, O.; Váša, L.; Wang, K.; Holly Rushmeier and Oliver Deussen
    Almost all mesh processing procedures cause some more or less visible changes in the appearance of objects represented by polygonal meshes. In many cases, such as mesh watermarking, simplification or lossy compression, the objective is to make the change in appearance negligible, or as small as possible, given some other constraints. Measuring the amount of distortion requires taking into account the final purpose of the data. In many applications, the final consumer of the data is a human observer, and therefore the perceptibility of the introduced appearance change by a human observer should be the criterion that is taken into account when designing and configuring the processing algorithms. In this review, we discuss the existing comparison metrics for static and dynamic (animated) triangle meshes. We describe the concepts used in perception-oriented metrics used for 2D image comparison, and we show how these concepts are employed in existing 3D mesh metrics. We describe the character of subjective data used for evaluation of mesh metrics and provide comparison results identifying the advantages and drawbacks of each method. Finally, we also discuss employing the perception-correlated metrics in perception-oriented mesh processing algorithms. Please use and the following text for graphical abstract: In this review, we discuss the existing comparison metrics for static and dynamic (animated) triangle meshes. We describe the concepts used in perception-oriented metrics used for 2D image comparison, and we show how these concepts are employed in existing 3D mesh metrics. We describe the character of subjective data used for evaluation of mesh metrics and provide comparison results identifying the advantages and drawbacks of each method. Finally, we also discuss employing the perception-correlated metrics in perception-oriented mesh processing algorithms.In this review, we discuss the existing comparison metrics for static and dynamic (animated) triangle meshes. We describe the concepts used in perception-oriented metrics used for 2D image comparison, and we show how these concepts are employed in existing 3D mesh metrics. We describe the character of subjective data used for evaluation of mesh metrics and provide comparison results identifying the advantages and drawbacks of each method. Finally, we also discuss employing the perception-correlated metrics in perception-oriented mesh processing algorithms.
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    Visualization and Analysis of Second-Order Tensors: Moving Beyond the Symmetric Positive-Definite Case
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Kratz, A.; Auer, C.; Stommel, M.; Hotz, I.; Holly Rushmeier and Oliver Deussen
    Tensors provide a powerful language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as the final result of simulations or as intermediate product. Due to their complexity, tensors are hard to interpret. This motivates the development of well-conceived visualization methods. As a sub-branch of scientific visualization, tensor field visualization has been especially pushed forward by diffusion tensor imaging. In this review, we focus on second-order tensors that are not diffusion tensors. Until now, these tensors, which might be neither positive-definite nor symmetric, are under-represented in visualization and existing visualization tools are often not appropriate for these tensors. Hence, we discuss the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them. The goal of this paper is to reveal the importance of the field and to encourage the development of new visualization methods for tensors from various application fields.Tensors provide a powerful language to describe physical phenomena. In this review, we focus on second-order tensors that are not diffusionensors. Until now, these tensors, which might be neither positive-definite nor symmetric, are underrepresented in visualization and existing visualization tools are often not appropriate for these tensors. Hence, we discuss the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them. The goal of this paper is to reveal the importance of the field and to encourage the development of new visualization methods for tensors from various application fields.
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    Just-in-Time Texture Synthesis
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Wang, Lili; Shi, Yulong; Chen, Yi; Popescu, Voicu; Holly Rushmeier and Oliver Deussen
    Texture bombing is a texture synthesis approach that saves memory by stopping short of assembling the output texture from the arrangement of input texture patches; instead, the arrangement is used directly at run time to texture surfaces. However, several problems remain in need of better solutions. One problem is improving texture diversification. A second problem is that mipmapping cannot be used because texel data is not stored explicitly. The lack of an appropriate level-of-detail (LoD) scheme results in severe minification artefacts. We present a just-in-time texturing method that addresses these two problems. Texture diversification is achieved by modelling a texture patch as an umbrella, a versatile hybrid 3-D geometry and texture structure with parameterized appearance. The LoD is adapted continuously with a hierarchical algorithm that acts directly on the arrangement map. Results show that our method can model and render the diversity present in nature with only small texture memory requirements.We present a just-intime texturing method that addresses these two problems. Texture diversification is achieved by modeling a texture patch as an umbrella, a versatile hybrid 3-D geometry and texture structure with parameterized appearance. The LoD is adapted continuously with a hierarchical algorithm that acts directly on the arrangement map. Results show that our method can model and render the diversity present in nature with only small texture memory requirements.
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    Efficient GPU Data Structures and Methods to Solve Sparse Linear Systems in Dynamics Applications
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Weber, Daniel; Bender, Jan; Schnoes, Markus; Stork, Andre; Fellner, Dieter W.; Holly Rushmeier and Oliver Deussen
    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.We present GPU data structures and algorithms to efficiently solve sparse linear systems which are typically required in simulations of multibody 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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    Simulation of Morphology Changes in Drying Leaves
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Jeong, SoHyeon; Park, Si-Hyung; Kim, Chang-Hun; Holly Rushmeier and Oliver Deussen
    We introduce a biologically motivated simulation technique for the realistic shape deformation of drying leaves. In contrast to skeleton-based leaf deformation, our approach simulates the whole leaf surface to capture the fine details of desiccated leaves. We represent a leaf as a triangulated double-layer structure that consists of a Delaunay triangulation discretized along the vein structure and its corresponding Voronoi diagram. This structure can generate not only sharp creases along leaf veins, but also the complicated curling and crumpling on the leaf surface. The loss of water is the major factor that controls the inhomogeneous shrinkage of drying leaves. The proposed osmotic water flow successfully models the gradual changes of dehydrated regions advancing towards the veins. We demonstrate the robustness of our method by comparing a sequence of simulated morphology changes with photographs of real leaves.We introduce a biologically motivated simulation technique for the realistic shape deformation of drying leaves. In contrast to skeleton-based leaf deformation, our approach simulates the whole leaf surface to capture the fine details of desiccated leaves. We represent a leaf as a triangulated double-layer structure that consists of a Delaunay triangulation discretized along the vein structure and its corresponding Voronoi diagram. This structure can generate not only sharp creases along leaf veins, but also the complicated curling and crumpling on the leaf surface. The loss of water is the major factor that controls the inhomogeneous shrinkage of drying leaves.
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    2013 Cover Image: Prism
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Spencer, Ben; Jones, Mark W.; Holly Rushmeier and Oliver Deussen
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    Scalable Symmetry Detection for Urban Scenes
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) Kerber, J.; Bokeloh, M.; Wand, M.; Seidel, H.-P.; Holly Rushmeier and Oliver Deussen
    In this paper, we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which has only been demonstrated on data sets of a few hundred megabytes maximum, our method scales to very large scenes: We map the detection problem to a nearest-eighbour problem in a low-dimensional feature space, and follow this with a cascade of tests for geometric clustering of potential matches. Our algorithm robustly handles noisy real-world scanner data, obtaining a recognition performance comparable to that of state-of-the-art methods. In practice, it scales linearly with scene size and achieves a high absolute throughput, processing half a terabyte of scanner data overnight on a dual socket commodity PC.In this paper we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which has only been demonstrated on data sets of a few hundred megabytes maximum, our method scales to very large scenes: We map the detection problem to a nearest-eighbor problem in a lowdimensional feature space, and follow this with a cascade of tests for geometric clustering of potential matches. Our algorithm robustly handles noisy real-world scanner data, obtaining a recognition performance comparable to that of state-of-the-art methods. In practice, it scales linearly with scene size and achieves a high absolute throughput, processing half a terabyte of scanner data overnight on a dual socket commodity PC.