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Item PriMo: Coupled Prisms for Intuitive Surface Modeling(The Eurographics Association, 2006) Botsch, Mario; Pauly, Mark; Gross, Markus; Kobbelt, Leif; Alla Sheffer and Konrad PolthierWe present a new method for 3D shape modeling that achieves intuitive and robust deformations by emulating physically plausible surface behavior inspired by thin shells and plates. The surface mesh is embedded in a layer of volumetric prisms, which are coupled through non-linear, elastic forces. To deform the mesh, prisms are rigidly transformed to satisfy user constraints while minimizing the elastic energy. The rigidity of the prisms prevents degenerations even under extreme deformations, making the method numerically stable. For the underlying geometric optimization we employ both local and global shape matching techniques. Our modeling framework allows for the specification of various geometrically intuitive parameters that provide control over the physical surface behavior. While computationally more involved than previous methods, our approach significantly improves robustness and simplifies user interaction for large, complex deformations.Item Fast Arbitrary Splitting of Deforming Objects(The Eurographics Association, 2006) Steinemann, Denis; Otaduy, Miguel A.; Gross, Markus; Marie-Paule Cani and James O'BrienWe present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. We propose the use of a meshless discretization of the deformation field, and a novel visibility graph for fast update of shape functions in meshless discretizations. We decompose the splitting operation into a first step where we synthesize crack surfaces as triangle meshes, and a second step where we use the newly synthesized surfaces to update the visibility graph, and thus the meshless discretization of the deformation field. The separation of the splitting operation into two steps, along with our novel visibility graph, enables high flexibility and control over the splitting trajectories, provides fast dynamic update of the meshless discretization, and facilitates an easy implementation, making our algorithm scalable, versatile, and suitable for a large range of applications, from computer animation to interactive medical simulation.We present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. We propose the use of a meshless discretization of the deformation field, and a novel visibility graph for fast update of shape functions in meshless discretizations. We decompose the splitting operation into a first step where we synthesize crack surfaces as triangle meshes, and a second step where we use the newly synthesized surfaces to update the visibility graph, and thus the meshless discretization of the deformation field. The separation of the splitting operation into two steps, along with our novel visibility graph, enables high flexibility and control over the splitting trajectories, provides fast dynamic update of the meshless discretization, and facilitates an easy implementation, making our algorithm scalable, versatile, and suitable for a large range of applications, from computer animation to interactive medical simulation.Item Fast Simulation of Deformable Models in Contact Using Dynamic Deformation Textures(The Eurographics Association, 2006) Galoppo, Nico; Otaduy, Miguel A.; Mecklenburg, Paul; Gross, Markus; Lin, Ming C.; Marie-Paule Cani and James O'BrienWe present an efficient algorithm for simulating contacts between deformable bodies with high-resolution surface geometry using dynamic deformation textures, which reformulate the 3D elastoplastic deformation and collision handling on a 2D parametric atlas to reduce the extremely high number of degrees of freedom in such a computa- tionally demanding simulation. We perform proximity queries for deformable bodies using a two-stage algorithm directly on dynamic deformation textures, resulting in output-sensitive collision detection that is independent of the combinatorial complexity of the deforming meshes. We present a robust, parallelizable formulation for computing constraint forces using implicit methods that exploits the structure of the motion equations to achieve highly stable simulation, while taking large time steps with inhomogeneous materials. The dynamic deformation textures can also be used directly for real-time shading and can easily be implemented using SIMD architecture on commodity hardware. We show that our approach, complementing existing pioneering work, offers significant computational advantages on challenging contact scenarios in dynamic simulation of deformable bodies.Item GPU-Based Ray-Casting of Quadratic Surfaces(The Eurographics Association, 2006) Sigg, Christian; Weyrich, Tim; Botsch, Mario; Gross, Markus; Mario Botsch and Baoquan Chen and Mark Pauly and Matthias ZwickerQuadratic surfaces are frequently used primitives in geometric modeling and scientific visualization, such as rendering of tensor fields, particles, and molecular structures. While high visual quality can be achieved using sophisticated ray tracing techniques, interactive applications typically use either coarsely tessellated polygonal approximations or pre-rendered depth sprites, thereby trading off visual quality and perspective correctness for higher rendering performance. In contrast, we propose an efficient rendering technique for quadric primitives based on GPU-accelerated splatting. While providing similar performance as point-sprites, our methods provides perspective correctness and superior visual quality using per-pixel ray-casting.Item Versatile Virtual Materials Using Implicit Connectivity(The Eurographics Association, 2006) Wicke, Martin; Hatt, Philipp; Pauly, Mark; Müller, Matthias; Gross, Markus; Mario Botsch and Baoquan Chen and Mark Pauly and Matthias ZwickerWe propose a new method for strain computation in mesh-free simulations. Without storing connectivity information, we compute strain using local rest states that are implicitly defined by the current system configuration. Particles in the simulation are subject to restoring forces arranging them in a locally defined lattice. The orientation of the lattice is found using local shape matching techniques. The strain state of each particle can then be computed by comparing the actual positions of the neighboring particles to their assigned lattice positions. All necessary information needed to compute strains is contained in the current state of the simulation, no rest state or connectivity information is stored. Since no time integration is used to compute the strain state, errors cannot accumulate, and the method is well-suited for stiff materials. In order to simulate phase transitions, the strain computation can be integrated into an existing particle-based fluid simulation framework. Implementing phase transitions between liquid and solid states becomes simple and elegant, since no transfer of material between different representations is needed. Using the current neighborhood relationships, the model provides penalty-based inter-object and self-collision handling at no additional computational cost.