Chapter 4 Vortex detection - Computer Graphics and Visualization

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Chapter 3. Particle Tracing F B E H G A D C (a) Normal cell F B H D E A G C (b) Sheared cell Figure 3.10: One orientation of the tetrahedral 6-decomposition; the tetrahedra retain their relative positions. E H F G A D B C (a) Normal cell H D E F A G B C (b) Sheared cell Figure 3.11: Other orientation of the tetrahedral 6-decomposition; the tetrahedra retain their relative positions. 32
3.4. Particle tracing in unstructured grids typically traverses only 3 of the tetrahedra, regardless of which decomposition is being used. 3.4 Particle tracing in unstructured grids So far, the grids we have used have been structured grids, which are characterized by a regular grid topology: in 3D space, the grid always consists of Ð ¢ Ñ ¢ Ò cells, and for each cell it is known which are the neighbouring cells. In contrast, unstructured grids have an irregular topology, so it is not known in advance which neighbours a cell has (see also Section 2.1). While structured grids typically consist of quadrangles in 2D and hexahedra in 3D, unstructured grids often consist of triangles in 2D and tetrahedra in 3D, although unstructured grids of hexahedra also exist. Figure 3.12 shows an example of an unstructured grid, used in a Finite Element Analysis of a slice of a human skull [van den Broek et al., 1998]. Figure 3.12: Unstructured grid from Finite Element Analysis An advantage of unstructured grids is the greater degree of modelling freedom. A disadvantage of unstructured grids is the greater complexity of certain algorithmic operations. Especially point location and grid traversal are difficult, because they rely on a stepwise traversal between neighbouring cells, but information about cell neighbours is not available in these grids. What is therefore necessary, is the addition of extra adjacency information for each cell. One way to do this is to derive and store information about cell faces, such that an algorithm can query the data structure to find the answers to the following questions: 1. which faces belong to a cell? 2. which cells are on either side of a face? Figure 3.13 shows the standard and additional information that can be added to handle unstructured grids. The standard information typically consists of a list of 33
Page 2 and 3: Extraction and Visualization of Geo
Page 4 and 5: Extraction and Visualization of Geo
Page 6 and 7: Preface The research described in t
Page 8 and 9: Contents 1 Introduction 1 1.1 Scien
Page 10 and 11: Contents 6.2.4 Vortex detection wit
Page 12 and 13: Chapter 1. Introduction Figure 1.1:
Page 14 and 15: Chapter 2 Geometry extraction techn
Page 16 and 17: 2.1. Fields and grids their geometr
Page 18 and 19: 2.3. Surfaces ¯ hyperstreamline: a
Page 20 and 21: 2.3. Surfaces in a local coordinate
Page 22 and 23: 2.4. Deformable models from some in
Page 24 and 25: 2.4. Deformable models where ÜÖ
Page 26 and 27: 2.5. Vortices There are several imp
Page 28 and 29: 2.5. Vortices contours called Simpl
Page 30 and 31: Chapter 3. Particle Tracing initial
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Page 78 and 79: Chapter 5 Deformable surfaces ÁÒ
Page 80 and 81: Surface Creation Surface Deformatio
Page 82 and 83: normvelo a= velo/len(velo) velograd
Page 84 and 85: 5.3.1 Node displacement 5.3. Surfac
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5.4. Surface refinement high cost f
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5.5. Examples Figure 5.11: Miller
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(a) shape after 17 iterations (b) s
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velorot a= rot(velo) velohd a= dot(
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5.5. Examples Figure 5.20: Final de
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Chapter 6 Applications This chapter
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Figure 6.1: PaciÞc Ocean; streamli
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y 80 70 60 50 40 30 20 10 0 0 20 40
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y 80 70 60 50 40 30 20 10 0 0 20 40
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(a) Top view of a horizontal grid s
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(a) Frame 0 (b) Frame 40 6.2. The B
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(a) Vorticity magnitude (b) Normali
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y 6130 6120 6110 6100 6090 6080 607
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Number of clusters 15 Number of CW
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(a) (b) 6.3. A transitional pipe ß
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(a) Ô (b) (c) (d) É 6.3. A tran
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Figure 6.19: isosurface of high É
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Figure 6.21: Selective streamlines
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Deformable surfaces with scalar cri
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6.4. The Delta-Wing aircraft (a) In
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Chapter 7. Conclusions and future w
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Chapter 7. Conclusions and future w
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Bibliography EKATERINIS, J.A., & SC
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Bibliography MILLER, J.V. 1990. On
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Bibliography SADARJOEN, I.A., VAN W
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Colour Plates 135
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Colour Plates Colour Plate 3: Backw
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Colour Plates Colour Plate 7: Pipe
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Summary this method offers the capa
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Samenvatting methode gebaseerd op k
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