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Item Robust Filtering of Noisy Scattered Point Data(The Eurographics Association, 2005) Schall, Oliver; Belyaev, Alexander; Seidel, Hans-Peter; Marc Alexa and Szymon Rusinkiewicz and Mark Pauly and Matthias ZwickerIn this paper, we develop a method for robust filtering of a noisy set of points sampled from a smooth surface. The main idea of the method consists of using a kernel density estimation technique for point clustering. Specifically, we use a mean-shift based clustering procedure. With every point of the input data we associate a local likelihood measure capturing the probability that a 3D point is located on the sampled surface. The likelihood measure takes into account the normal directions estimated at the scattered points. Our filtering procedure suppresses noise of different amplitudes and allows for an easy detection of outliers which are then automatically removed by simple thresholding. The remaining set of maximum likelihood points delivers an accurate point-based approximation of the surface. We also show that while some established meshing techniques often fail to reconstruct the surface from original noisy point scattered data, they work well in conjunction with our filtering method.Item Modeling Liquidus Hypersurfaces through Simplicial Complexes(The Eurographics Association, 2010) Natali, Mattia; Attene, Marco; Ottonello, Giulio; Enrico Puppo and Andrea Brogni and Leila De FlorianiThis paper describes an operational pipeline that exploits computational geometry to derive useful knowledge about the crystallization behaviour of materials composed of varying amounts of pure components. Starting from existing knowledge related to the pure components, we compute the Gibbs free energy of all their possible compositions in a given range of temperatures, both in liquid and solid phases. Then, we exploit the convex hull method to derive the coexistence of solid and liquid phases, and model the resulting liquidus hypersurface as a simplicial complex. On such a complex, we propose novel tools to robustly compute descent lines describing the crystallization path induced by heat loss for any initial composition in the system.Item An Improved Discrete Level of Detail Model Through an Incremental Representation(The Eurographics Association, 2010) Ribelles, Jose; López, Angeles; Belmonte, Oscar; John Collomosse and Ian GrimsteadReal-time applications such as computer and video games, virtual reality and scientific simulation require rendering of complex models for realism. Graphics rendering engines include multiresolution modelling techniques to accelerate the visualization process. The Discrete Level of Detail framework (DLoD) is usually the most popular while the Continuous Level of Detail framework (CLoD) is still not as widely used by software developers. In this paper, we first discuss the benefits and drawbacks of both frameworks. Then, we present a model based on coding a discrete number of levels of detail (LoDs), with more LoDs coded than is usual in DLoD, and with an incremental representation, which is often used in CLoD. This model obtains a performance similar to DLoD by providing optimized LoDs for efficient visualization, while the popping effect is imperceptible. We present specific proposals for each of the three main stages involved in multiresolution processing: geometry simplification, construction of the incremental representation and retrieval of either uniform or view-dependent LoDs.Item Topology Preserving Surface Extraction Using Adaptive Subdivision(The Eurographics Association, 2004) Varadhan, Gokul; Krishnan, Shankar; Sriram, TVN; Manocha, Dinesh; Roberto Scopigno and Denis ZorinWe address the problem of computing a topology preserving isosurface from a volumetric grid using Marching Cubes for geometry processing applications. We present a novel topology preserving subdivision algorithm to generate an adaptive volumetric grid. Our algorithm ensures that every grid cell satisfies two local geometric criteria: a complex cell criterion and a star-shaped criterion. We show that these two criteria are sufficient to ensure that the surface extracted from the grid using Marching Cubes has the same genus and connectedness as that of the exact isosurface. We use our subdivision algorithm for accurate boundary evaluation of CSG combinations of polyhedra and low degree algebraic primitives, translational motion planning, model simplification and remeshing. The running time of our algorithm varies between a few seconds for simple models composed of a few thousand triangles to tens of seconds for complex polyhedral models represented using hundreds of thousands of triangles.Item Spherical Barycentric Coordinates(The Eurographics Association, 2006) Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter; Alla Sheffer and Konrad PolthierWe develop spherical barycentric coordinates. Analogous to classical, planar barycentric coordinates that describe the positions of points in a plane with respect to the vertices of a given planar polygon, spherical barycentric coordinates describe the positions of points on a sphere with respect to the vertices of a given spherical polygon. In particular, we introduce spherical mean value coordinates that inherit many good properties of their planar counterparts. Furthermore, we present a construction that gives a simple and intuitive geometric interpretation for classical barycentric coordinates, like Wachspress coordinates, mean value coordinates, and discrete harmonic coordinates. One of the most interesting consequences is the possibility to construct mean value coordinates for arbitrary polygonal meshes. So far, this was only possible for triangular meshes. Furthermore, spherical barycentric coordinates can be used for all applications where only planar barycentric coordinates were available up to now. They include Bézier surfaces, parameterization, free-form deformations, and interpolation of rotations.Item An Edge-based Approach to Adaptively Refining a Mesh for Cloth Deformation(The Eurographics Association, 2009) Simnett, Timothy J. R.; Laycock, Stephen D.; Day, Andy M.; Wen Tang and John CollomosseSimulating cloth in real-time is a challenging endeavour due to the number of triangles necessary to depict the potentially frequent changes in curvature, in combination with the physics calculations which model the deformations. To alleviate the costs, adaptive methods are often employed to refine the mesh in areas of high curvature, however, they do not often consider a decimation or coarsening of areas which were refined previously. In addition to this, the triangulation and consistency checks required to maintain a continuous mesh can be prohibitively time consuming when attempting to simulate larger pieces of cloth. In this paper we present an efficient edge-based approach to adaptively refine and coarsen a dynamic mesh, with the aim to exploit the varied nature of cloth by trading the level of detail in flat parts for increased detail in the curved regions of the cloth. An edge-based approach enables fast incremental refinement and coarsening, whereby only two triangles need updating on each split or join of an edge. The criteria for refinement includes curvature, edge length and edge collisions. Simple collision detection is performed allowing interactions between the cloth and the other objects in the environment.Item Meshing Point Clouds Using Spherical Parameterization(The Eurographics Association, 2004) Zwicker, M.; Gotsman, C.; Markus Gross and Hanspeter Pfister and Marc Alexa and Szymon RusinkiewiczWe present a simple method for meshing a 3D point cloud to a manifold genus-0 mesh. Our approach is based on recent methods for spherical embedding of planar graphs, where we use instead a k-nearest neighborhood graph of the point cloud. Our approach proceeds in two steps: We first embed the neighborhood graph on a sphere using an iterative procedure, minimizing the tangential Laplacian. Then we triangulate the embedded points and apply the resulting mesh connectivity to the input points. Besides meshing, spherical embedding of point clouds may also be used for other applications such as texture mapping or morphing.Item Elastic Secondary Deformations by Vector Field Integration(The Eurographics Association, 2007) Funck, Wolfram von; Theisel, Holger; Seidel, Hans-Peter; Alexander Belyaev and Michael GarlandWe present an approach for elastic secondary deformations of shapes described as triangular meshes. The deformations are steered by the simulation of a low number of simple mass-spring sets. The result of this simulation is used to define time-dependent divergence-free vector fields whose numerical path line integration gives the new location of each vertex. This way the deformation is guaranteed to be volume-preserving and without self-intersections, giving plausible elastic deformations. Due to a GPU implementation, the deformation can be obtained in real-time for fairly complex shapes. The approach also avoids unwanted intersections in the case of collisions in the primary animation. We demonstrate its accuracy, stableness and usefulness for different kinds of primary animations/deformations.Item Heat Diffusion Approach for Feature-based Body Scans Analysis(The Eurographics Association, 2011) Lovato, Christian; Zancanaro, C.; Castellani, Umberto; Giachetti, Andrea; H. Laga and T. Schreck and A. Ferreira and A. Godil and I. Pratikakis and R. VeltkampIn this paper we propose the use of spectral shape analysis techniques for selection and classification of anthro- pometric points extracted from human-body scans. Few feature points are detected by exploiting the capability of heat diffusion process in capturing the extremities of surface protrusions which are often related to anthropometric landmarks. Then, a heat kernel signature is computed for each feature point which are associated to its seman- tic group by employing a learning-by-example procedure exploiting manual point labeling provided by an expert anthropometrist. Detected points are not clearly the same precise anatomical locations used in standard anthro- pometric procedures, but their matching can be useful for different applications like automatic model registration or simple body type evaluation. Experimental tests carried out on several subjects with different anthropometric characteristics show encouraging results demonstrating the potential usefulness of the approach as well as the necessity of further investigation on point description and matching.Item A Benchmarking Framework for Static Collision Detection(The Eurographics Association, 2008) Diktas, Engin Deniz; Sahiner, Ali Vahit; Ik Soo Lim and Wen TangPerformanceof static collision detection queries depends on the type of the hierarchy chosen as well as the relative positioning of the colliding objects. In order to evaluate the performance of bounding volume hierarchies, relevant criteria that affect the query performance need to be determined and the sample space should be generated accordingly. In this paper we present a benchmarking framework for evaluating the performance of various static collision detection algorithms. In this framework, instances of a moving rigid object are placed on the surface of another instance of the same object fixed at a certain position, where the contact occurs for the first time. Then by offsetting the surface inwards (outwards) we generate new surfaces that are at a certain fixed negative (positive) distance to the original surface. Placing the moving object on these offset surfaces makes the object penetrate (approach) the fixed object at a fixed distance. For offset surface generation we create a signed distance field and run marching cubes algorithm on it.