The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Christoph Schär - One of the best experts on this subject based on the ideXlab platform.
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On potential vorticity flux vectors
Journal of the Atmospheric Sciences, 2003Co-Authors: Peter R. Bannon, Jürg Schmidli, Christoph SchärAbstract:Abstract Dynamical, rather than kinematical, considerations indicate that a generalized potential vorticity in terms of the gradient of an arbitrary Scalar Function requires that the potential vorticity flux vector contain a contribution due to gravity and the pressure gradient force. It is shown that such a potential vorticity flux vector has a simpler definition in terms of the gradient of the kinetic energy rather than that of a Bernoulli Function. This result is valid for multicomponent fluids. Flux vectors for a salty ocean and a moist atmosphere with hydrometeors are presented.
Peter R. Bannon - One of the best experts on this subject based on the ideXlab platform.
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On potential vorticity flux vectors
Journal of the Atmospheric Sciences, 2003Co-Authors: Peter R. Bannon, Jürg Schmidli, Christoph SchärAbstract:Abstract Dynamical, rather than kinematical, considerations indicate that a generalized potential vorticity in terms of the gradient of an arbitrary Scalar Function requires that the potential vorticity flux vector contain a contribution due to gravity and the pressure gradient force. It is shown that such a potential vorticity flux vector has a simpler definition in terms of the gradient of the kinetic energy rather than that of a Bernoulli Function. This result is valid for multicomponent fluids. Flux vectors for a salty ocean and a moist atmosphere with hydrometeors are presented.
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NOTES AND CORRESPONDENCE On Potential Vorticity Flux Vectors
2003Co-Authors: Peter R. BannonAbstract:Dynamical, rather than kinematical, considerations indicate that a generalized potential vorticity in terms of the gradient of an arbitrary Scalar Function requires that the potential vorticity flux vector contain a contribution due to gravity and the pressure gradient force. It is shown that such a potential vorticity flux vector has a simpler definition in terms of the gradient of the kinetic energy rather than that of a Bernoulli Function. This result is valid for multicomponent fluids. Flux vectors for a salty ocean and a moist atmosphere with hydrometeors are presented.
Bianca Falcidieno - One of the best experts on this subject based on the ideXlab platform.
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Defining, contouring, and visualizing Scalar Functions on point-sampled surfaces
Computer-Aided Design, 2011Co-Authors: Giuseppe Patanè, Bianca FalcidienoAbstract:This paper addresses the definition, contouring, and visualization of Scalar Functions on unorganized point sets, which are sampled from a surface in 3D space; the proposed framework builds on moving least-squares techniques and implicit modeling. Given a Scalar Function f:P->R, defined on a point set P, the idea behind our approach is to exploit the local connectivity structure of the k-nearest neighbor graph of P and mimic the contouring of Scalar Functions defined on triangle meshes. Moving least-squares and implicit modeling techniques are used to extend f from P to the surface M underlying P. To this end, we compute an analytical approximation f@? of f that allows us to provide an exact differential analysis of f@?, draw its iso-contours, visualize its behavior on and around M, and approximate its critical points. We also compare moving least-squares and implicit techniques for the definition of the Scalar Function underlying f and discuss their numerical stability and approximation accuracy. Finally, the proposed framework is a starting point to extend those processing techniques that build on the analysis of Scalar Functions on 2-manifold surfaces to point sets.
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Topology- and error-driven extension of Scalar Functions from surfaces to volumes
ACM Transactions on Graphics, 2009Co-Authors: Giuseppe Patanè, Michela Spagnuolo, Bianca FalcidienoAbstract:The behavior of a variety of phenomena measurable on the boundary of 3D shapes is studied by modeling the set of known measurements as a Scalar Function f :P → R, defined on a surface P. Furthermore, the large amount of scientific data calls for efficient techniques to correlate, describe, and analyze this data. In this context, we focus on the problem of extending the measures captured by a Scalar Function f, defined on the boundary surface P of a 3D shape, to its surrounding volume. This goal is achieved by computing a sequence of volumetric Functions that approximate f up to a specified accuracy and preserve its critical points. More precisely, we compute a smooth map g : R3 → R such that the piecewise linear Function h :egP : P → R, which interpolates the values of g at the vertices of the triangulated surface P, is an approximation of f with the same critical points. In this way, we overcome the limitation of traditional approaches to Function approximation, which are mainly based on a numerical error estimation and do not provide measurements of the topological and geometric features of f. The proposed approximation scheme builds on the properties of f related to its global structure, that is, its critical points, and ignores the local details of f, which can be successively introduced according to the target approximation accuracy.
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Technical Section: Computing smooth approximations of Scalar Functions with constraints
Computers & Graphics, 2009Co-Authors: Giuseppe Patanè, Bianca FalcidienoAbstract:In engineering, geographical applications, scientific visualization, and bio-informatics, a variety of phenomena is described by a large set of data modeled as the values of a Scalar Function f:M->R defined on a surface M. A low quality of the discrete representations of the input data, unstable computations, numerical approximations, and noise might produce Functions with a high number of critical points. In this context, we propose an algorithmic framework for smoothing an arbitrary Scalar Function, while simplifying its redundant critical points and preserving those that are mandatory for its description. From our perspective, the critical points of f are a natural choice to guide the approximation scheme; in fact, they usually represent relevant information about the behavior of f or the shape itself. To address the aforementioned aims, we compute a smooth approximation f@?:M->R of f whose set of critical points contains those that have been preserved by the simplification process. The idea behind the proposed approach is to combine smoothing techniques, critical points, and spectral properties of the Laplacian matrix. Inserting constraints in the smoothing of f allows us to overcome the traditional error-driven approximation of f, which does not provide constraints on the preserved topological features. Finally, the computational cost of the proposed approach is O(nlogn), where n is the number of vertices of M.
Giuseppe Patanè - One of the best experts on this subject based on the ideXlab platform.
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Mesh-based and meshless design and approximation of Scalar Functions
Computer Aided Geometric Design, 2017Co-Authors: Giuseppe PatanèAbstract:In engineering, geographical applications, bio-informatics, and scientific visualisation, a variety of phenomena is described by data modelled as the values of a Scalar Function defined on a surface or a volume, and critical points (i.e., maxima, minima, saddles) usually represent a relevant information about the input data or an underlying phenomenon. Furthermore, the distribution of the critical points is crucial for geometry processing and shape analysis; e.g., for controlling the number of patches in quadrilateral remeshing and the number of nodes of Reeb graphs and Morse–Smale complexes. In this context, we address the design of a smooth Function, whose maxima, minima, and saddles are selected by the user or imported from a template (e.g., Laplacian eigenFunctions, diffusion maps). In this way, we support the selection of the saddles of the resulting Function and not only its extrema, which is one of the main limitations of previous work. Then, we discuss the meshless approximation of an input Scalar Function by preserving its persistent critical points and its local behaviour, as encoded by the spatial distribution and shape of the level-sets. Both problems are addressed by computing an implicit approximation with radial basis Functions, which is independent of the discretisation of differential operators and of assumptions on the sampling of the input domain. This approximation allows us to introduce a meshless iso-contouring and classification of the critical points, which are characterised in terms of the differential properties of the meshless approximation and of the geometry of the input surface, as encoded by its first and second fundamental form. Furthermore, the computation is performed at an arbitrary resolution by locally refining the input surface and by applying differential calculus to the meshless approximation. As main applications, we consider the approximation and analysis of Scalar Functions on both 3D shapes and volumes in graphics, Geographic Information Systems, medicine, and bio-informatics.
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Defining, contouring, and visualizing Scalar Functions on point-sampled surfaces
Computer-Aided Design, 2011Co-Authors: Giuseppe Patanè, Bianca FalcidienoAbstract:This paper addresses the definition, contouring, and visualization of Scalar Functions on unorganized point sets, which are sampled from a surface in 3D space; the proposed framework builds on moving least-squares techniques and implicit modeling. Given a Scalar Function f:P->R, defined on a point set P, the idea behind our approach is to exploit the local connectivity structure of the k-nearest neighbor graph of P and mimic the contouring of Scalar Functions defined on triangle meshes. Moving least-squares and implicit modeling techniques are used to extend f from P to the surface M underlying P. To this end, we compute an analytical approximation f@? of f that allows us to provide an exact differential analysis of f@?, draw its iso-contours, visualize its behavior on and around M, and approximate its critical points. We also compare moving least-squares and implicit techniques for the definition of the Scalar Function underlying f and discuss their numerical stability and approximation accuracy. Finally, the proposed framework is a starting point to extend those processing techniques that build on the analysis of Scalar Functions on 2-manifold surfaces to point sets.
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Topology- and error-driven extension of Scalar Functions from surfaces to volumes
ACM Transactions on Graphics, 2009Co-Authors: Giuseppe Patanè, Michela Spagnuolo, Bianca FalcidienoAbstract:The behavior of a variety of phenomena measurable on the boundary of 3D shapes is studied by modeling the set of known measurements as a Scalar Function f :P → R, defined on a surface P. Furthermore, the large amount of scientific data calls for efficient techniques to correlate, describe, and analyze this data. In this context, we focus on the problem of extending the measures captured by a Scalar Function f, defined on the boundary surface P of a 3D shape, to its surrounding volume. This goal is achieved by computing a sequence of volumetric Functions that approximate f up to a specified accuracy and preserve its critical points. More precisely, we compute a smooth map g : R3 → R such that the piecewise linear Function h :egP : P → R, which interpolates the values of g at the vertices of the triangulated surface P, is an approximation of f with the same critical points. In this way, we overcome the limitation of traditional approaches to Function approximation, which are mainly based on a numerical error estimation and do not provide measurements of the topological and geometric features of f. The proposed approximation scheme builds on the properties of f related to its global structure, that is, its critical points, and ignores the local details of f, which can be successively introduced according to the target approximation accuracy.
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Technical Section: Computing smooth approximations of Scalar Functions with constraints
Computers & Graphics, 2009Co-Authors: Giuseppe Patanè, Bianca FalcidienoAbstract:In engineering, geographical applications, scientific visualization, and bio-informatics, a variety of phenomena is described by a large set of data modeled as the values of a Scalar Function f:M->R defined on a surface M. A low quality of the discrete representations of the input data, unstable computations, numerical approximations, and noise might produce Functions with a high number of critical points. In this context, we propose an algorithmic framework for smoothing an arbitrary Scalar Function, while simplifying its redundant critical points and preserving those that are mandatory for its description. From our perspective, the critical points of f are a natural choice to guide the approximation scheme; in fact, they usually represent relevant information about the behavior of f or the shape itself. To address the aforementioned aims, we compute a smooth approximation f@?:M->R of f whose set of critical points contains those that have been preserved by the simplification process. The idea behind the proposed approach is to combine smoothing techniques, critical points, and spectral properties of the Laplacian matrix. Inserting constraints in the smoothing of f allows us to overcome the traditional error-driven approximation of f, which does not provide constraints on the preserved topological features. Finally, the computational cost of the proposed approach is O(nlogn), where n is the number of vertices of M.
Jürg Schmidli - One of the best experts on this subject based on the ideXlab platform.
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On potential vorticity flux vectors
Journal of the Atmospheric Sciences, 2003Co-Authors: Peter R. Bannon, Jürg Schmidli, Christoph SchärAbstract:Abstract Dynamical, rather than kinematical, considerations indicate that a generalized potential vorticity in terms of the gradient of an arbitrary Scalar Function requires that the potential vorticity flux vector contain a contribution due to gravity and the pressure gradient force. It is shown that such a potential vorticity flux vector has a simpler definition in terms of the gradient of the kinetic energy rather than that of a Bernoulli Function. This result is valid for multicomponent fluids. Flux vectors for a salty ocean and a moist atmosphere with hydrometeors are presented.
