Chapter 4 Vortex detection - Computer Graphics and Visualization

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Deformable surfaces with scalar criteria 6.4. The Delta-Wing aircraft The extraction of vortex tubes proceeds in two steps: the Þrst step uses a selection criterion to Þnd the vortex core, which is then used to initialize a deformable surface. The second step uses a deformation criterion to Þnd the outer surface of the vortex tube. For both steps, we can distinguish two types of criteria: scalar criteria and vector criteria. The Þrst type will be covered in the current section, the other in the next section. In accordance with the scheme in Section 5.1, the following steps were performed: ¯ Region selection: the quantity used here is pressure Ô. The selection criterion is minimal pressure, Ô ¡ ÑÒ Ô , where is a user-deÞnable parameter. The result is shown in Figure 6.24a, where the selected points are again shown as cross marks. ¯ Initial Surface Creation: in the selected regions, integral attributes are calculated, which results in the ellipsoid shown in Figure 6.24b. The ratios of the ellipsoid axes result in a 1D object, the cylinder shown in Figure 6.24c. ¯ Surface deformation: for the deformation stage, again Ô is used. The result is therefore a local isosurface of Ô. Figure 6.24d shows the resulting vortex tube after one iteration with the single-step step size determination method. It consists of 180 triangles. This surface takes 3.1 s to generate on an SGI Indy, which makes it suitable for use as an interactive tool. Deformable surfaces with vector criteria We also used other criteria, based on additional (vector) quantities, to extract the vortex tube from the same data set. Again following the scheme in Section 5.1, these steps were performed: ¯ Region Selection: the vortex tube extraction now uses additional physical quantities, which have been derived from the original quantities in the data set: the vorticity vector Þeld and its magnitude . These were also used in [Banks & Singer, 1994; Villasenor & Vincent, 1992]. The criterion used for the initialization is: low pressure and high vorticity magnitude: Ô ¡ÑÒ Ô and ¡ÑÜ where and are user-deÞnable parameters. ¯ Initial Surface Creation: in the selected region, integral attributes are calculated which result in an ellipsoid. The ratios of the ellipsoid axes result in a 1D object, the cylinder shown in Figure 6.26a. The colour indicates cost function, where red is highest and blue is lowest. ¯ Surface Deformation: the deformation criterion uses the angle between the vorticity vector at the vortex core and the vorticity vector × at a node Ò of the deformable surface: « × . Figure 6.25 shows that « at the core. The algorithm makes the surface grow in the direction where this « Æ ,oras high as possible but lower than Æ . Since the cost function is deÞned as Ó× «, and « Æ , minimizing the cost function maximizes the angle: ÜÒ Ó× × (6.1) 119
Chapter 6. Applications (a) Selected nodes (b) Selected nodes and Þtted ellipsoid (c) Initial vortex tube (d) Final vortex tube Figure 6.24: Delta-Wing; extraction of a vortex tube with scalar deformation criteria 120 n ωs α ω c Figure 6.25: Delta-Wing; vortex-Þnding with vector criteria
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Extraction and Visualization of Geo
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Extraction and Visualization of Geo
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Preface The research described in t
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Contents 1 Introduction 1 1.1 Scien
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Contents 6.2.4 Vortex detection wit
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Chapter 1. Introduction Figure 1.1:
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Chapter 2 Geometry extraction techn
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2.1. Fields and grids their geometr
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2.3. Surfaces ¯ hyperstreamline: a
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2.3. Surfaces in a local coordinate
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2.4. Deformable models from some in
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2.4. Deformable models where ÜÖ
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2.5. Vortices There are several imp
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2.5. Vortices contours called Simpl
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Chapter 3. Particle Tracing initial
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Chapter 3. Particle Tracing a decre
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Chapter 3. Particle Tracing 3.3 Par
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Chapter 3. Particle Tracing Figure
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Chapter 3. Particle Tracing (a) h =
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Chapter 3. Particle Tracing F B E H
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Chapter 3. Particle Tracing 44 Figu
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Chapter 3. Particle Tracing Figure
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Chapter 4. Vortex detection 4.1 Phy
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Chapter 4. Vortex detection Figure
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Chapter 4. Vortex detection (a) (b)
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Chapter 4. Vortex detection indicat
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Chapter 4. Vortex detection 4.3.2 E
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Chapter 4. Vortex detection 58 Figu
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Chapter 4. Vortex detection p 1 α
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Page 116 and 117: Number of clusters 15 Number of CW
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Page 124 and 125: Figure 6.21: Selective streamlines
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Page 134 and 135: Bibliography EKATERINIS, J.A., & SC
Page 136 and 137: Bibliography MILLER, J.V. 1990. On
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Page 146 and 147: Summary this method offers the capa
Page 148 and 149: Samenvatting methode gebaseerd op k
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