HECKEL, B., WEBER, G., HAMANN, B., AND JOY, K. I. 1999. Construction of vector field hierarchies. Proc. Visualization '99, IEEE Computer Society Press, pp. 19-25.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on the screen. Selected streamline drawings are furthermore considered by Jobard et al. [10] Recently, two approaches for clustering vector data have been proposed. In both approaches a hierarchical clustering tree is produced and the resulting clusters are visualized with arrows. Heckel et al. [9] start from scattered points with vector data. Initially all points are stored in a single cluster, which is recursively split in a top down manner. At each step, the cluster with the strongest discrepancy between streamlines generated by the original field and its approximation by the cluster is ....

....vector field remains visible in the clustering (see [23] for details) This may be seen as an advantage of the discrete clustering method, see Fig. 18. Finally, the shapes produced by the continuous clustering are not constrained to simple convex ones, as in the method presented by Heckel et al. [9]. We have applied the continuous clustering method also to the visualization of 3D fields. Fig. 17 shows the visualization of a 3D circular vortex field from two different viewpoints. The produced arrow icons illustrate the clustering of the data in the center of the domain, where the flow is ....

B. Heckel, G. Weber, B. Hamann, and K. I. Joy. Construction of vector field hierarchies. Proc. IEEE Visualization '99, IEEE Computer Society Press, pp. 19--25, 1999.

....on the screen. Selected streamline drawings are furthermore considered by Jobard et al. 9] Recently, two approaches for clustering vector data have been proposed. In both approaches a hierarchical clustering tree is produced and the resulting clusters are visualized with arrows. Heckel et al. [8] start from scattered points with vector data. Initially all points are stored in a single cluster, which is recursively split in a top down manner. At each step, the cluster with the strongest discrepancy between streamlines generated by the original field and its harald tpreuss ....

....vector field remains visible in the clustering (see [21] for details) This may be seen as an advantage of the discrete clustering method, see Fig. 11. Finally, the shapes produced by the continuous clustering are not constrained to simple convex ones, as in the method presented by Heckel et al. [8]. We have applied the continuous clustering method also to the visualization of 3D fields. Fig. 10 shows the visualization of a 3D circular vortex field from two different viewpoints. The produced arrow icons illustrate the clustering of the data in the center of the domain, where the flow is ....

B. Heckel, G. Weber, B. Hamann, and K. I. Joy. Construction of vector field hierarchies. Proc. Visualization '99, IEEE Computer Society Press, pp. 19-25, 1999.

....compare the original and the new vector field and consequently give information about the quality of the algorithms. The first approaches on metrics (distance measures) of vector fields consider local deviations of direction and magnitude of the flow vectors in a certain number of sample points ([Hecke99], Telea99] These distance functions give a fast comparison of the vector field but do not take the complete flow behavior into consideration. The application of topological methods is nowadays a popular method to visualize vector fields. Originally introduced in [Helma89] for 2D vector fields, ....

B. Heckel, G.H. Weber, B. Hamann, and K.I.Joy. Construction of vector field hierarchies. In D. Ebert, M. Gross, and B. Hamann, editors, Proc. IEEE Visualization '99, pages 19--26, Los Alamitos, 1999.

....number of streamlines computed and speeding up the LIC convolution, Stalling and Hege s new method can gain a great saving in computing the LIC. The main idea of this paper is to further speed up the LIC computation by adopting vector field simplification methods and hierarchical data structures [10, 11]. While the remaining of the paper discusses our algorithm for accelerating the standard LIC method, we believe that combining our algorithm with the fast LIC algorithm can be very effective. 1.2 Measure for simplification To allow different levels of approximations, we need to provide error ....

....to measure the parallelism between the streamlines, i.e. how the flow directions in a local region are similar to each other. We have implemented two measures to represent the complexity of the vector field. One is the magnitude of curl, and the other is the metric proposed by Heckel et al.[10]. Our goal is to make regions with features like vortices and saddle points have a high degree of complexity. Uninteresting parts such as straight flows, on the other hand, are considered to have a low degree of complexity. The measures are calculated for each point in the field at a ....

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B. Heckel, G. Weber, B Hamann, and K. Joy. Construction of vector field hierarchies. In Proceedings of Visualization '99, CA, 1999.

....on the screen. Selected streamline drawings are furthermore considered by Jobard et al. 9] Recently, two approaches for clustering vector data have been proposed. In both approaches a hierarchical clustering tree is produced and the resulting clusters are visualized with arrows. Heckel et al. [8] start from scattered points with vector data. Initially all points are stored in a single cluster, which is recursively split in a top down manner. At each step, the cluster with the strongest discrepancy between streamlines generated by the original field and its [harald j tpreuss j rumpf j ....

....vector field remains visible in the clustering (see [21] for details) This may be seen as an advantage of the discrete clustering method, see Fig. 11. Finally, the shapes produced by the continuous clustering are not constrained to simple convex ones, as in the method presented by Heckel et al. [8]. We have applied the continuous clustering method also to the visualization of 3D fields. Fig. 10 shows the visualization of a 3D circular vortex field from two different viewpoints. The produced arrow icons illustrate the clustering of the data in the center of the domain, where the flow is ....

B. Heckel, G. Weber, B. Hamann, and K. I. Joy. Construction of vector field hierarchies. Proc. Visualization '99, IEEE Computer Society Press, pp. 19-25, 1999.

....grid representation of the original data set, and this is common in practice. Alternatively, a hierarchical, multiresolution representation of the data can be constructed using, for example, quadtrees or octrees [12,13,14] progressive meshes [15] wavelets [16] or other clustering approaches [17,18]. The cost of these methods does not significantly increase as the number of visualization tasks increases, but the amount of data that can be used is limited by the speed and memory of the local graphics workstation. Thus, as the overall problem size increases, the percentage of subsampled points ....

Bjoern Heckel, Gunther Weber, Bernd Hamann, and Kenneth Joy. Construction of vector field hierarchies. In Proceedings of IEEE Visualization 99, pages 19-26, October 1999.

....the original data. While in [26] stream line placement in 2D flows is guided by visual attributes, in [14] evenly spaced stream lines are generated based on a distance criterion but without explicit consideration of the flow topology. On the contrary, the main concern of the work presented in [10, 25] is to effectively simplify the underlying data without loss of relevant information. In general, however, these hierarchical techniques are local in that they usually consider only the vector field in the geometric neighborhood around each position, but do not take into account the global ....

B. Heckel, G. Weber, B. Hamann, and K. Joy. Construction of vector field hierarchies. In Proceedings IEEE Visualization 99, pages 19--27, 1999.

....representation of the original data set, and this is common in practice. Alternatively, a hierarchical, multiresolution representation of the data can be constructed using, for example, quadtrees or octrees [15, 11, 14] progressive meshes [13, 12] wavelets [23] or other clustering approaches [10, 25]. The level of detail in each region is controlled through a variety of mechanisms, such as error tolerance bounds that control fidelity to the original model, or user input, such as field of view. 1 We note that simply sending each image as the object is manipulated from the remote resources ....

Bjoern Heckel, Gunther Weber, Bernd Hamann, and Kenneth Joy. Construction of vector field hierarchies. In Proceedings of IEEE Visualization 99, pages 19--26, October 1999.

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HECKEL, B., WEBER, G. H., HAMANN, B., AND JOY, K. I. 1999. Construction of vector field hierarchies. In Proceedings IEEE Visualization '99, IEEE, San Francisco, CA, D. S. Ebert, M. Gross, and B. Hamann, Eds., IEEE, 19--26.

....data representation. This hierarchy can be derived from a clustering scheme. Clustering, see [1] is a classical data analysis technique commonly used in statistics. It has been applied to surface reconstruction by Heckel et al. 3] and this approach has been further generalized by Heckel et al. [4] for vector field simplification. In the context of vector field visualization, the basic idea is to partition a vector field into clusters corresponding to coherent regions characterized by vectors of similar direction and length. Each cluster has a representant. It is computed as average of all ....

....a given error metric is determined. 2. This cluster is split into two clusters. This process is iterated until the error of all clusters is below a given threshold and a simplified representation of a field has been obtained. A detailed description of the clustering process can be found in [4]. Instead of using the original data set, it is possible to use the representants of the clusters resulting from performing the split steps. By storing all intermediate clusters one has access to a hierarchical representation. 4 The clustering tree The clustering process yields a hierarchical ....

B. Heckel, G. H. Weber, B. Hamann, and Kenneth I. Joy. Construction of vector field hierarchies. To appear in Proceedings IEEE Visualization '99, IEEE Computer Society Press, Los Alamitos, October 1999.

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HECKEL, B., WEBER, G., HAMANN, B., AND JOY, K. I. 1999. Construction of vector field hierarchies. Proc. Visualization '99, IEEE Computer Society Press, pp. 19-25.

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B. Heckel, G. Weber, B. Hamann, and K. Joy, "Construction of vector field hierarchies," in Visualization '99, Proc. IEEE, pp. 19--27, 1999.

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Bjoern Heckel, Gunther H. Weber, Bernd Hamann, and Kenneth I. Joy. Construction of vector field hierarchies. In IEEE Visualization '99, pages 19--26, San Francisco, 1999. IEEE. 12

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