167 research outputs found

    Representing three-dimensional cross fields using 4th order tensors

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    This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in R9\mathbb{R}^9. The algebraic structure of the tensors and their projections on \mbox{SO}(3) are presented. The relationship of the new formulation with spherical harmonics is exposed. This paper is quite theoretical. Due to pages limitation, few practical aspects related to the computations of cross fields are exposed. Nevetheless, a global smoothing algorithm is briefly presented and computation of cross fields are finally depicted

    All-Hex Meshing of Multiple-Region Domains without Cleanup

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    AbstractIn this paper, we present a new algorithm for all-hex meshing of domains with multiple regions without post-processing cleanup. Our method starts with a strongly balanced octree. In contrast to snapping the grid points onto the geometric boundaries, we move points a slight distance away from the common boundaries. Then we intersect the moved grid with the geometry. This allows us to avoid creating any flat angles, and we are able to handle two-sided regions and more complex topologies than prior methods. The algorithm is robust and cleanup-free; without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is also more predictable than prior art

    Lp Centroidal Voronoi Tesselation and its applications

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    International audienceThis paper introduces Lp -Centroidal Voronoi Tessellation (Lp -CVT), a generalization of CVT that minimizes a higher-order moment of the coordinates on the Voronoi cells. This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy). Lp -CVT is computed by a quasi-Newton optimization framework, based on closed-form derivations of the objective function and its gradient. The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field). Applications to anisotropic, quad-dominant surface remeshing and to hex-dominant volume meshing are presented. Unlike previous work, Lp -CVT captures sharp features and intersections without requiring any pre-tagging

    The receding front method applied to hexahedral mesh generation of exterior domains

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    Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside–outside approach. On the other hand, advancing front methods generate high-quality hexahedra near the boundary using an outside–inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside–outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.Peer ReviewedPostprint (author's final draft

    Personalized modeling for real-time pressure ulcer prevention in sitting posture

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    , Ischial pressure ulcer is an important risk for every paraplegic person and a major public health issue. Pressure ulcers appear following excessive compression of buttock's soft tissues by bony structures, and particularly in ischial and sacral bones. Current prevention techniques are mainly based on daily skin inspection to spot red patches or injuries. Nevertheless, most pressure ulcers occur internally and are difficult to detect early. Estimating internal strains within soft tissues could help to evaluate the risk of pressure ulcer. A subject-specific biomechanical model could be used to assess internal strains from measured skin surface pressures. However, a realistic 3D non-linear Finite Element buttock model, with different layers of tissue materials for skin, fat and muscles, requires somewhere between minutes and hours to compute, therefore forbidding its use in a real-time daily prevention context. In this article, we propose to optimize these computations by using a reduced order modeling technique (ROM) based on proper orthogonal decompositions of the pressure and strain fields coupled with a machine learning method. ROM allows strains to be evaluated inside the model interactively (i.e. in less than a second) for any pressure field measured below the buttocks. In our case, with only 19 modes of variation of pressure patterns, an error divergence of one percent is observed compared to the full scale simulation for evaluating the strain field. This reduced model could therefore be the first step towards interactive pressure ulcer prevention in a daily setup. Highlights-Buttocks biomechanical modelling,-Reduced order model,-Daily pressure ulcer prevention

    Quad Meshing

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    Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing

    The First Multichroic Receiver and Results from ACTPol.

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    The Cosmic Microwave Background (CMB) is a unique and powerful tool for the study of cosmology and fundamental physics. The next frontier of CMB research is to extract the wealth of cosmological information available from its polarization. Accurate measurement of this polarization signal will enable us to probe inflation, provide an alternative means to measure the neutrino mass sum and number of neutrino species; improve our understanding of dark energy; explore the reionization history of our Universe; probe the large scale structure through gravitational lensing; and enable a multitude of other astrophysical studies. The polarized signatures of the early universe are extremely weak, dominated by foregrounds, and its measurement is susceptible to instrumental effects. Extracting the information contained in these faint signals requires instruments with high sensitivity, excellent control over systematic errors, and careful data analysis. The Atacama Cosmology Telescope Polarimeter (ACTPol) is a state-of-the-art experiment that measures CMB polarization over finer angular scales from the Atacama desert in Chile. In this thesis, I present an overview of this project and then describe my work on the project including development of a new polarization sensitive dichroic camera for ACTPol designed to increase the sensitivity of CMB telescopes and enable high precision measurements of CMB polarization; the development of novel metamaterial antireflection coatings for silicon lenses; diffraction from panel gaps; calibration of detector pass-bands; and a detailed description of my analysis of the polarization properties of extragalactic point sources discovered with the ACTPol data. I conclude with a discussion of the science of ACTPol, and the impact of my technical work on future CMB experiments.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135767/1/dattar_1.pd
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