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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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    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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    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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    Coarse-to-Fine Isometric Shape Correspondence by Tracking Symmetric Flips
    (The Eurographics Association and Blackwell Publishing Ltd., 2013) SahillioÄ lu, Y.; Yemez, Y.; Holly Rushmeier and Oliver Deussen
    We address the symmetric flip problem that is inherent to multi-resolution isometric shape matching algorithms. To this effect, we extend our previous work which handles the dense isometric correspondence problem in the original 3D Euclidean space via coarse-to-fine combinatorial matching. The key idea is based on keeping track of all optimal solutions, which may be more than one due to symmetry especially at coarse levels, throughout denser levels of the shape matching process. We compare the resulting dense correspondence algorithm with state-of-the-art techniques over several 3D shape benchmark datasets. The experiments show that our method, which is fast and scalable, is performance-wise better than or on a par with the best performant algorithms existing in the literature for isometric (or nearly isometric) shape correspondence. Our key idea of tracking symmetric flips can be considered as a meta-approach that can be applied to other multi-resolution shape matching algorithms, as we also demonstrate by experiments.We address the symmetric flip problem that is inherent to multiresolution isometric shape matching algorithms.To this effect, we extend our previous work which handles the dense isometric correspondence problem in the original 3D Euclidean space via coarse-to-fine combinatorial matching. The key idea is based on keeping track of all optimal solutions, which may be more than one due to symmetry especially at coarse levels, throughout denser levels of the shape matching process. We compare the resulting dense correspondence algorithm with state-of-the-art techniques over several 3D shape benchmark datasets. The experiments show that our method, which is fast and scalable, is performance-wise better than or on a par with the best performant algorithms existing in the literature for isometric (or nearly isometric) shape correspondence.