This paper proposes a Galilean invariant generalization of critical points of vector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extra...
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ISBN:
(纸本)9783642150135
This paper proposes a Galilean invariant generalization of critical points of vector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, like saddles and centers, and filters out short-living local structures. This is well suited for analysis of turbulent flow, where standard snapshot topology yields an unmanageable large number of topological structures that are barely related to the few main long-living features employed in conceptual fluid mechanics models. Results are shown for periodic and chaotic vortex motion.
The (apparent) contour of a smooth mapping from a 2-manifold to the plane, f: M -> R-2, is the set of critical values, that is, the image of the points at which the gradients of the two component functions are line...
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ISBN:
(纸本)9783642150135
The (apparent) contour of a smooth mapping from a 2-manifold to the plane, f: M -> R-2, is the set of critical values, that is, the image of the points at which the gradients of the two component functions are linearly dependent. Assuming M is compact and orientable and measuring difference with the erosion distance, we prove that the contour is stable.
Interfaces between materials with different mechanical properties play an important role in technical applications. Nowadays molecular dynamics simulations are used to observe the behavior of such compound materials a...
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ISBN:
(纸本)9783642150135
Interfaces between materials with different mechanical properties play an important role in technical applications. Nowadays molecular dynamics simulations are used to observe the behavior of such compound materials at the atomic level. Due to different atom crystal sizes, dislocations in the atom crystal structure occur once external forces are applied, and it has been observed that studying the change of these dislocations can provide further understanding of macroscopic attributes like elasticity and plasticity. Standard visualization techniques such as the rendering of individual atoms work for 2D data or sectional views;however, visualizing dislocations in 3D using such methods usually fail due to occlusion and clutter. In this work we propose to extract and visualize the structure of dislocations, which summarizes the commonly employed filtered atomistic renderings into a concise representation. The benefits of our approach are clearer images while retaining relevant data and easier visual tracking of topological changes over time.
We present a user-assisted approach to extracting and visualizing structural features from point clouds obtained by terrestrial and airborne laser scanning devices. We apply a multi-scale approach to express the membe...
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ISBN:
(纸本)9783642150135
We present a user-assisted approach to extracting and visualizing structural features from point clouds obtained by terrestrial and airborne laser scanning devices. We apply a multi-scale approach to express the membership of local point environments to corresponding geometric shape classes in terms of probability. This information is filtered and combined to establish feature graphs which can be visualized in combination with the color-encoded feature and structural probability estimates of the measured raw point data. Our method can be used, for example, for exploring geological point data scanned from multiple viewpoints.
Contour, split and join trees can be defined as functors acting on the category of scalar fields, whose morphisms are value-preserving functions. The categorical definition provides a natural way to efficiently comput...
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ISBN:
(纸本)9783642150135
Contour, split and join trees can be defined as functors acting on the category of scalar fields, whose morphisms are value-preserving functions. The categorical definition provides a natural way to efficiently compute a variety of topological properties of all contours, sublevel or superlevel components in a scalar field. The result is a labeling of the contour, split or join tree and can be used to find all contours, sublevel or superlevel sets with desired properties. We describe an algorithm for airway segmentation from Computed Tomography (CT) scans based on this paradigm. It computes all sublevel components in thick slices of the input image that have simple topology and branching structure. The output is a connected component of the union of all such sublevel components. This procedure can be viewed as a local thresholding approach, where the local thresholds are determined based on topological analysis of sublevel sets.
We describe a combinatorial streaming algorithm to extract features which identify regions of local intense rates of mixing in two terascale turbulent combustion simulations. Our algorithm allows simulation data compr...
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ISBN:
(纸本)9783642150135
We describe a combinatorial streaming algorithm to extract features which identify regions of local intense rates of mixing in two terascale turbulent combustion simulations. Our algorithm allows simulation data comprised of scalar fields represented on 728x896x512 or 2025x1600x400 grids to be processed on a single relatively lightweight machine. The turbulence-induced mixing governs the rate of reaction and hence is of principal interest in these combustion simulations. We use our feature extraction algorithm to compare two very different simulations and find that in both the thickness of the extracted features grows with decreasing turbulence intensity. Simultaneous consideration of results of applying the algorithm to the HO2 mass fraction field indicates that autoignition kernels near the base of a lifted flame tend not to overlap with the high mixing rate regions.
We propose a topology-based segmentation of 2D symmetric tensor fields, which results in cells bounded by tensorlines. We are particularly interested in the influence of the interpolation scheme on the topology, consi...
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ISBN:
(纸本)9783642150135
We propose a topology-based segmentation of 2D symmetric tensor fields, which results in cells bounded by tensorlines. We are particularly interested in the influence of the interpolation scheme on the topology, considering eigenvector-based and component-wise linear interpolation. When using eigenvector-based interpolation the most significant modification to the standard topology extraction algorithm is the insertion of additional vertices at degenerate points. A subsequent Delaunay re-triangulation leads to connections between close degenerate points. These new connections create degenerate edges and triangles. When comparing the resulting topology per triangle with the one obtained by component-wise linear interpolation the results are qualitatively similar, but our approach leads to a less "cluttered" segmentation.
The Morse-Smale complex is an effective topology-based representation for identifying, ordering, and selectively removing features in scalar-valued data. Several algorithms are known for its effective computation, how...
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ISBN:
(纸本)9783642150135
The Morse-Smale complex is an effective topology-based representation for identifying, ordering, and selectively removing features in scalar-valued data. Several algorithms are known for its effective computation, however, common problems pose practical challenges for any feature-finding approach using the Morse-Smale complex. We identify these problems and present practical solutions: (1) we identify the cause of spurious critical points due to simulation of simplicity, and present a general technique for solving it;(2) we improve simplification performance by reordering critical point cancellation operations and introducing an efficient data structure for storing the arcs of the complex;(3) we present a practical approach for handling boundary conditions.
Ambient isotopic approximations are fundamental for correct representation of the embedding of geometric objects in R-3, with a detailed geometric construction given here. Using that geometry, an algorithm is presente...
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ISBN:
(纸本)9783642150135
Ambient isotopic approximations are fundamental for correct representation of the embedding of geometric objects in R-3, with a detailed geometric construction given here. Using that geometry, an algorithm is presented for efficient update of these isotopic approximations for dynamic visualization with a molecular simulation.
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