Search results for: geodesics

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geodesics</title> <meta name="description" content="Search results for: geodesics"> <meta name="keywords" content="geodesics"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" 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id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="geodesics"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 6</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: geodesics</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6</span> Riemannain Geometries Of Visual Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jacek%20Turski">Jacek Turski</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The visual space geometries are constructed in the Riemannian geometry framework from simulated iso-disparity conics in the horizontalvisual plane of the binocular system with the asymmetric eyes (AEs). For the eyes fixating at the abathic distance, which depends on the AE鈥檚 parameters, the iso-disparity conics are frontal straight lines in physical space. For allother fixations, the iso-disparity conics consist of families of the ellipses or hyperbolas depending on both the AE鈥檚 parameters and the bifoveal fixation. However, the iso-disparity conic鈥檚 arcs are perceived in the gaze direction asthe frontal lines and are referred to as visual geodesics. Thus, geometriesof physical and visual spaces are different. A simple postulate that combines simulated iso-disparity conics with basic anatomy od the human visual system gives the relative depth for the fixation at the abathic distance that establishes the Riemann matric tensor. The resulting geodesics are incomplete in the gaze direction and, therefore, give thefinite distances to the horizon that depend on the AE鈥檚 parameters. Moreover, the curvature vanishes in this eyes posture such that visual space is flat. For all other fixations, only the sign of the curvature canbe inferred from the global behavior of the simulated iso-disparity conics: the curvature is positive for the elliptic iso-disparity curves and negative for the hyperbolic iso-disparity curves. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymmetric%20eye%20model" title="asymmetric eye model">asymmetric eye model</a>, <a href="https://publications.waset.org/abstracts/search?q=iso-disparity%20conics" title=" iso-disparity conics"> iso-disparity conics</a>, <a href="https://publications.waset.org/abstracts/search?q=metric%20tensor" title=" metric tensor"> metric tensor</a>, <a href="https://publications.waset.org/abstracts/search?q=geodesics" title=" geodesics"> geodesics</a>, <a href="https://publications.waset.org/abstracts/search?q=curvature" title=" curvature"> curvature</a> </p> <a href="https://publications.waset.org/abstracts/144276/riemannain-geometries-of-visual-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/144276.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">145</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5</span> Approximation of Geodesics on Meshes with Implementation in Rhinoceros Software</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Marian%20Sagat">Marian Sagat</a>, <a href="https://publications.waset.org/abstracts/search?q=Mariana%20Remesikova"> Mariana Remesikova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In civil engineering, there is a problem how to industrially produce tensile membrane structures that are non-developable surfaces. Nondevelopable surfaces can only be developed with a certain error and we want to minimize this error. To that goal, the non-developable surfaces are cut into plates along to the geodesic curves. We propose a numerical algorithm for finding approximations of open geodesics on meshes and surfaces based on geodesic curvature flow. For practical reasons, it is important to automatize the choice of the time step. We propose a method for automatic setting of the time step based on the diagonal dominance criterion for the matrix of the linear system obtained by discretization of our partial differential equation model. Practical experiments show reliability of this method. Because approximation of the model is made by numerical method based on classic derivatives, it is necessary to solve obstacles which occur for meshes with sharp corners. We solve this problem for big family of meshes with sharp corners via special rotations which can be seen as partial unfolding of the mesh. In practical applications, it is required that the approximation of geodesic has its vertices only on the edges of the mesh. This problem is solved by a specially designed pointing tracking algorithm. We also partially solve the problem of finding geodesics on meshes with holes. We implemented the whole algorithm in Rhinoceros (commercial 3D computer graphics and computer-aided design software ). It is done by using C# language as C# assembly library for Grasshopper, which is plugin in Rhinoceros. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=geodesic" title="geodesic">geodesic</a>, <a href="https://publications.waset.org/abstracts/search?q=geodesic%20curvature%20flow" title=" geodesic curvature flow"> geodesic curvature flow</a>, <a href="https://publications.waset.org/abstracts/search?q=mesh" title=" mesh"> mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=Rhinoceros%20software" title=" Rhinoceros software"> Rhinoceros software</a> </p> <a href="https://publications.waset.org/abstracts/93093/approximation-of-geodesics-on-meshes-with-implementation-in-rhinoceros-software" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/93093.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">151</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4</span> Some Properties of Cut Locus of a Flat Torus</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pakkinee%20Chitsakul">Pakkinee Chitsakul</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cut%20locus" title="cut locus">cut locus</a>, <a href="https://publications.waset.org/abstracts/search?q=flat%20torus" title=" flat torus"> flat torus</a>, <a href="https://publications.waset.org/abstracts/search?q=geodesics" title=" geodesics "> geodesics </a> </p> <a href="https://publications.waset.org/abstracts/3028/some-properties-of-cut-locus-of-a-flat-torus" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3028.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">330</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3</span> Enhanced Tensor Tomographic Reconstruction: Integrating Absorption, Refraction and Temporal Effects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lukas%20Vierus">Lukas Vierus</a>, <a href="https://publications.waset.org/abstracts/search?q=Thomas%20Schuster"> Thomas Schuster</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat鈥檚 principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=attenuated%20refractive%20dynamic%20ray%20transform%20of%20tensor%20fields" title="attenuated refractive dynamic ray transform of tensor fields">attenuated refractive dynamic ray transform of tensor fields</a>, <a href="https://publications.waset.org/abstracts/search?q=geodesics" title=" geodesics"> geodesics</a>, <a href="https://publications.waset.org/abstracts/search?q=transport%20equation" title=" transport equation"> transport equation</a>, <a href="https://publications.waset.org/abstracts/search?q=viscosity%20solutions" title=" viscosity solutions"> viscosity solutions</a> </p> <a href="https://publications.waset.org/abstracts/184677/enhanced-tensor-tomographic-reconstruction-integrating-absorption-refraction-and-temporal-effects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184677.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">51</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2</span> Poisson Type Spherically Symmetric Spacetimes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gonzalo%20Garc%C3%ADa-Reyes">Gonzalo Garc铆a-Reyes</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Conformastat spherically symmetric exact solutions of Einstein's field equations representing matter distributions made of fluid both perfect and anisotropic from given solutions of Poisson's equation of Newtonian gravity are investigated. The approach is used in the construction of new relativistic models of thick spherical shells and three-component models of galaxies (bulge, disk, and dark matter halo), writing, in this case, the metric in cylindrical coordinates. In addition, the circular motion of test particles (rotation curves) along geodesics on the equatorial plane of matter configurations and the stability of the orbits against radial perturbations are studied. The models constructed satisfy all the energy conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=general%20relativity" title="general relativity">general relativity</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=spherical%20symmetry" title=" spherical symmetry"> spherical symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=galaxy" title=" galaxy"> galaxy</a>, <a href="https://publications.waset.org/abstracts/search?q=kinematics%20and%20dynamics" title=" kinematics and dynamics"> kinematics and dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=dark%20matter" title=" dark matter"> dark matter</a> </p> <a href="https://publications.waset.org/abstracts/151913/poisson-type-spherically-symmetric-spacetimes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151913.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">87</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1</span> A Nonlocal Means Algorithm for Poisson Denoising Based on Information Geometry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dongxu%20Chen">Dongxu Chen</a>, <a href="https://publications.waset.org/abstracts/search?q=Yipeng%20Li"> Yipeng Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an information geometry NonlocalMeans(NLM) algorithm for Poisson denoising. NLM estimates a noise-free pixel as a weighted average of image pixels, where each pixel is weighted according to the similarity between image patches in Euclidean space. In this work, every pixel is a Poisson distribution locally estimated by Maximum Likelihood (ML), all distributions consist of a statistical manifold. A NLM denoising algorithm is conducted on the statistical manifold where Fisher information matrix can be used for computing distribution geodesics referenced as the similarity between patches. This approach was demonstrated to be competitive with related state-of-the-art methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=image%20denoising" title="image denoising">image denoising</a>, <a href="https://publications.waset.org/abstracts/search?q=Poisson%20noise" title=" Poisson noise"> Poisson noise</a>, <a href="https://publications.waset.org/abstracts/search?q=information%20geometry" title=" information geometry"> information geometry</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal-means" title=" nonlocal-means"> nonlocal-means</a> </p> <a href="https://publications.waset.org/abstracts/51221/a-nonlocal-means-algorithm-for-poisson-denoising-based-on-information-geometry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51221.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">285</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>

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Search results for: geodesics