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Item Functional Webs for Freeform Architecture(The Eurographics Association and Blackwell Publishing Ltd., 2011) Deng, B.; Pottmann, Helmut; Wallner, Johannes; Mario Botsch and Scott SchaeferRationalization and construction-aware design dominate the issue of realizability of freeform architecture. The former means the decomposition of an intended shape into parts which are sufficiently simple and efficient to manufacture; the latter refers to a design procedure which already incorporates rationalization. Recent contributions to this topic have been concerned mostly with small-scale parts, for instance with planar faces of meshes. The present paper deals with another important aspect, namely long-range parts and supporting structures. It turns out that from the pure geometry viewpoint this means studying families of curves which cover surfaces in certain well-defined ways. Depending on the application one has in mind, different combinatorial arrangements of curves are required. We here restrict ourselves to so-called hexagonal webs which correspond to a triangular or tri-hex decomposition of a surface. The individual curve may have certain special properties, like being planar, being a geodesic, or being part of a circle. Each of these properties is motivated by manufacturability considerations and imposes constraints on the shape of the surface. We investigate the available degrees of freedom, show numerical methods of optimization, and demonstrate the effectivity of our approach and the variability of construction solutions derived from webs by means of actual architectural designs.Item A Multiscale Metric for 3D Mesh Visual Quality Assessment(The Eurographics Association and Blackwell Publishing Ltd., 2011) Lavoué, Guillaume; Mario Botsch and Scott SchaeferMany processing operations are nowadays applied on 3D meshes like compression, watermarking, remeshing and so forth; these processes are mostly driven and/or evaluated using simple distortion measures like the Hausdorff distance and the root mean square error, however these measures do not correlate with the human visual perception while the visual quality of the processed meshes is a crucial issue. In that context we introduce a full-reference 3D mesh quality metric; this metric can compare two meshes with arbitrary connectivity or sampling density and produces a score that predicts the distortion visibility between them; a visual distortion map is also created. Our metric outperforms its counterparts from the state of the art, in term of correlation with mean opinion scores coming from subjective experiments on three existing databases. Additionally, we present an application of this new metric to the improvement of rate-distortion evaluation of recent progressive compression algorithms.Item Interactive Exploration of Polymer-Solvent Interactions(The Eurographics Association, 2011) Thomaß, Bertram; Walter, Jonathan; Krone, Michael; Hasse, Hans; Ertl, Thomas; Peter Eisert and Joachim Hornegger and Konrad PolthierThe interaction of three-dimensional linked hydrophilic polymers with surrounding solvents in time-dependent data sets is of great interest for domain experts and current research in molecular dynamics. These polymers are called hydrogels, and their most characteristic property is their swelling in aqueous solutions by absorbing the solvent. Their conformation transition can be studied by investigations of the interaction of the single polymer strand and the solvent directly around the polymer at an atomistic level. We present new visualization techniques to interactively study time-dependent data sets from molecular dynamics simulations-with special regard to polymer-solvent interactions like local concentrations and hydrogen bonds-as well as filtering methods to facilitate analysis. Such methods that visualize polymer-solvent interactions on a hydration shell around a polymer are not available in current tools and can greatly facilitate the visual analysis, which helps domain experts to extract additional information about hydrogel characteristics and gain new insights from the simulation results. While our visual analysis methods presented in this paper clearly facilitate the analysis of hydrogels and lead to new insight, the presented concepts are applicable to other domains like proteins or polymers in general that interact with solvents.Item Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces(The Eurographics Association and Blackwell Publishing Ltd., 2011) Szymczak, Andrzej; H. Hauser, H. Pfister, and J. J. van WijkNumerical simulations and experimental observations are inherently imprecise. Therefore, most vector fields of interest in scientific visualization are known only up to an error. In such cases, some topological features, especially those not stable enough, may be artifacts of the imprecision of the input. This paper introduces a technique to compute topological features of user-prescribed stability with respect to perturbation of the input vector field. In order to make our approach simple and efficient, we develop our algorithms for the case of piecewise constant (PC) vector fields. Our approach is based on a super-transition graph, a common graph representation of all PC vector fields whose vector value in a mesh triangle is contained in a convex set of vectors associated with that triangle. The graph is used to compute a Morse decomposition that is coarse enough to be correct for all vector fields satisfying the constraint. Apart from computing stable Morse decompositions, our technique can also be used to estimate the stability of Morse sets with respect to perturbation of the vector field or to compute topological features of continuous vector fields using the PC framework.Item CubeCover - Parameterization of 3D Volumes(The Eurographics Association and Blackwell Publishing Ltd., 2011) Nieser, Matthias; Reitebuch, Ulrich; Polthier, Konrad; Mario Botsch and Scott SchaeferDespite the success of quad-based 2D surface parameterization methods, effective parameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. CUBECOVER is a first approach for generating a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field. The input of CUBECOVER is a tetrahedral volume mesh. First, a frame field is designed with manual input from the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and the hexahedral mesh are computed so as to align with the given frame field. CUBECOVER has similarities to the QUADCOVER algorithm and extends it from 2D surfaces to 3D volumes. The paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties of the appropriate function space.Item Skeleton Computation of Orthogonal Polyhedra(The Eurographics Association and Blackwell Publishing Ltd., 2011) Martinez, Jonas; Vigo, Marc; Pla-Garcia, Nuria; Mario Botsch and Scott SchaeferSkeletons are powerful geometric abstractions that provide useful representations for a number of geometric operations. The straight skeleton has a lower combinatorial complexity compared with the medial axis. Moreover, while the medial axis of a polyhedron is composed of quadric surfaces the straight skeleton just consist of planar faces. Although there exist several methods to compute the straight skeleton of a polygon, the straight skeleton of polyhedra has been paid much less attention. We require to compute the skeleton of very large datasets storing orthogonal polyhedra. Furthermore, we need to treat geometric degeneracies that usually arise when dealing with orthogonal polyhedra. We present a new approach so as to robustly compute the straight skeleton of orthogonal polyhedra. We follow a geometric technique that works directly with the boundary of an orthogonal polyhedron. Our approach is output sensitive with respect to the number of vertices of the skeleton and solves geometric degeneracies. Unlike the existing straight skeleton algorithms that shrink the object boundary to obtain the skeleton, our algorithm relies on the plane sweep paradigm. The resulting skeleton is only composed of axis-aligned and 45 rotated planar faces and edges.Item Deformable 3D Shape Registration Based on Local Similarity Transforms(The Eurographics Association and Blackwell Publishing Ltd., 2011) Papazov, Chavdar; Burschka, Darius; Mario Botsch and Scott SchaeferIn this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as-rigid-as-possible deformations but also local and global scale. We formulate an ordinary differential equation (ODE) which describes the transition of a source shape towards a target shape. We assume that both shapes are roughly pre-aligned (e.g., frames of a motion sequence). The ODE consists of two terms. The first one causes the deformation by pulling the source shape points towards corresponding points on the target shape. Initial correspondences are estimated by closestpoint search and then refined by an efficient smoothing scheme. The second term regularizes the deformation by drawing the points towards locally defined rest positions. These are given by the optimal similarity transform which matches the initial (undeformed) neighborhood of a source point to its current (deformed) neighborhood. The proposed ODE allows for a very efficient explicit numerical integration. This avoids the repeated solution of large linear systems usually done when solving the registration problem within general-purpose non-linear optimization frameworks. We experimentally validate the proposed method on a variety of real data and perform a comparison with several state-of-the-art approaches.Item Instant Level-of-Detail(The Eurographics Association, 2011) Grund, Nico; Derzapf, Evgenij; Guthe, Michael; Peter Eisert and Joachim Hornegger and Konrad PolthierHighly detailed models are commonly used in computer games and other interactive rendering applications. In this context, static levels-of-detail are frequently used to achieve real-time frame rates. While this is a simple solution to improve the rendering performance, the additional geometry needs to be stored and loaded into graphics memory. This is especially problematic in online applications, where the data needs to be transmitted over a possibly slow connection. On the other hand, consumer level computers are usually equipped with a graphics card that can be used for general purpose parallel computing. Based on this observation, we propose a high-quality parallel mesh simplification algorithm based on the quadric error metric. The simplification performance can compete with the time required to load additional meshes from a local hard disk.Item A Hierarchical Grid Based Framework for Fast Collision Detection(The Eurographics Association and Blackwell Publishing Ltd., 2011) Fan, Wenshan; Wang, Bin; Paul, Jean-Claude; Sun, Jiaguang; Mario Botsch and Scott SchaeferWe present a novel hierarchical grid based method for fast collision detection (CD) for deformable models on GPU architecture. A two-level grid is employed to accommodate the non-uniform distribution of practical scene geometry. A bottom-to-top method is implemented to assign the triangles into the hierarchical grid without any iteration while a deferred scheme is introduced to efficiently update the data structure. To address the issue of load balancing, which greatly influences the performance in SIMD parallelism, a propagation scheme which utilizes a parallel scan and a segmented scan is presented, distributing workloads evenly across all concurrent threads. The proposed method supports both discrete collision detection (DCD) and continuous collision detection (CCD) with self-collision. Some typical benchmarks are tested to verify the effectiveness of our method. The results highlight our speedups over prior algorithms on different commodity GPUs.Item A Multiscale Approach to Optimal Transport(The Eurographics Association and Blackwell Publishing Ltd., 2011) Mérigot, Quentin; Mario Botsch and Scott SchaeferIn this paper, we propose an improvement of an algorithm of Aurenhammer, Hoffmann and Aronov to find a least square matching between a probability density and finite set of sites with mass constraints, in the Euclidean plane. Our algorithm exploits the multiscale nature of this optimal transport problem. We iteratively simplify the target using Lloyd's algorithm, and use the solution of the simplified problem as a rough initial solution to the more complex one. This approach allows for fast estimation of distances between measures related to optimal transport (known as Earth-mover or Wasserstein distances). We also discuss the implementation of these algorithms, and compare the original one to its multiscale counterpart.