Chapter 4 Vortex detection - Computer Graphics and Visualization

More documents

Recommendations

Info

Chapter 2 Geometry extraction techniques Bengawan Solo, . . . 1 Mata airmu dari Solo terkurung gunung seribu Air mengalir sampai jauh akhirnya ke laut. This chapter reviews related work concerning geometry extraction. The purposes of this chapter are to show the context of our work and to provide a basis for the discussions in the following chapters. As stated in Chapter 1, it is possibly to classify visualization techniques as direct techniques, geometric techniques, and feature-based techniques [Post et al., 1999]. The focus in this thesis is on geometric techniques, although sometimes we employ elements from feature-based techniques as well. Geometric techniques produce geometries, which have two important advantages: ¯ geometries are easy for people to interpret. The visual system of the human brain is well adapted to recognizing shapes and colour properties of geometries like surfaces and curves. ¯ geometries are easy for computers to display. Modern hardware systems of computers are specialized in rendering lines and surfaces with colours and textures, to create a clear representation. Several important types of geometries are: ¯ curves ¯ surfaces ¯ solids ¯ deformable models Curves are often used to get a global view of the flow field. Surfaces are often used to get a local view of specific surface features, such as stream surfaces or separation surfaces. Deformable models are a special type of curves and surfaces, which start from some initial shape, and grow or shrink towards some target shape of a feature. In addition, a vortex is not a type of geometry, but a type of feature in fluid flows, which may be represented by various types of geometries, such as curves and surfaces. The remainder of this chapter is organized as follows. Section 2.1 gives definitions of several kinds of data fields and grids. Section 2.2 describes various flow curves, 1 Solo River, ...//Yoursource is in Solo // confined by a thousand mountains // Your water flows quite far // and finally into the sea. (Indonesian traditional) 5
Chapter 2. Geometry extraction techniques and Section 2.3 various flow surfaces. Section 2.4 covers deformable models. Finally, Section 2.5 describes techniques for vortex detection. 2.1 Fields and grids 2.1.1 Fields A three-dimensional field can be represented analytically by a global function Ü Ý Þ , defined over a bounded spatial domain in Ê [Silver et al., 1999]. A unique field value × at every point Ü Ý Þ of the domain can be found by evaluation: × Ü Ý Þ everywhere in the domain. This is usually not the case with the discrete numerical fields that are more common in science and engineering, where data values are known only at a finite number of data points. Such discrete fields are usually generated by data acquisition systems or numerical computer simulations. Measured data fields can be generated by medical imaging systems, such as computed tomography (CT), magnetic resonance imaging (MRI), or positron emission tomography (PET) scanners. Other sources of large measured data fields include remote sensing systems of satellites, scanning electron microscopes, and seismic and acoustic sensing for underwater observations. For simplicity, we will assume in the rest of this thesis that the data fields have been generated by numerical simulations. Physical models often consist of partial differential equations that cannot be solved globally and analytically. Therefore, discrete methods such as finite elements, finite differences, or finite volume methods are often used to numerically solve local equations. These methods are based on defining a computational grid, consisting of nodes and cells. Approximated equations are specified, resulting in a system of equations that can be solved numerically at each grid node or cell. The domain of a simulation may have two or three spatial dimensions. It may also be varying in time. The data points (or grid points) thus are 2D Ü Ý or 3D Ü Ý Þ coordinate positions. The data fields may contain any combination of scalar quantities (e.g. pressure, density, or temperature), vector quantities (e.g. force or velocity), or tensor quantities (e.g. stress or deformation) at each data point. The data values may be constant in time, or vary as a function of time. Time-dependent fields are important for highly dynamic phenomena such as fluid flow. 2.1.2 Grids There are many types of computational grids, depending on the simulation technique, the domain, and the application [Silver et al., 1999]. A grid consists of nodes and cells. The nodes are points defined in the simulation domain, and the cells are simple spatial elements connecting the nodes: triangles or quadrangles in 2D, tetrahedra or hexahedra in 3D. The cells must fill the whole domain, but may not intersect or overlap, and adjacent cells must have common edges and faces. Grids can be classified according to 6
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 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
Page 32 and 33: Chapter 3. Particle Tracing a decre
Page 34 and 35: Chapter 3. Particle Tracing 3.3 Par
Page 36 and 37: Chapter 3. Particle Tracing Figure
Page 38 and 39: Chapter 3. Particle Tracing (a) h =
Page 40 and 41: Chapter 3. Particle Tracing F B E H
Page 42 and 43: Chapter 3. Particle Tracing nodes w
Page 44 and 45: Chapter 3. Particle Tracing 3.5 Exa
Page 46 and 47: Chapter 3. Particle Tracing (a) fra
Page 48 and 49: Chapter 3. Particle Tracing 4.249 4
Page 50 and 51: Chapter 3. Particle Tracing 42 (a)
Page 52 and 53: Chapter 3. Particle Tracing 44 Figu
Page 54 and 55: Chapter 3. Particle Tracing Figure
Page 56 and 57: Chapter 4. Vortex detection 4.1 Phy
Page 58 and 59: Chapter 4. Vortex detection Figure
Page 60 and 61: Chapter 4. Vortex detection (a) (b)
Page 62 and 63: Chapter 4. Vortex detection indicat
Page 64 and 65:
Chapter 4. Vortex detection 4.3.2 E
Page 66 and 67:
Chapter 4. Vortex detection 58 Figu
Page 68 and 69:
Chapter 4. Vortex detection Figure
Page 70 and 71:
Chapter 4. Vortex detection Û. Unf
Page 72 and 73:
Chapter 4. Vortex detection y 6 4 2
Page 74 and 75:
Chapter 4. Vortex detection p 1 α
Page 76 and 77:
Chapter 4. Vortex detection (a) (c)
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
Page 86 and 87:
5.3. Surface deformation of the ran
Page 88 and 89:
C λ l λ 3 λ 2 λ 1 λ r λ 5.4.
Page 90 and 91:
5.4. Surface refinement high cost f
Page 92 and 93:
5.5. Examples Figure 5.11: Miller
Page 94 and 95:
(a) shape after 17 iterations (b) s
Page 96 and 97:
velorot a= rot(velo) velohd a= dot(
Page 98 and 99:
5.5. Examples Figure 5.20: Final de
Page 100 and 101:
Chapter 6 Applications This chapter
Page 102 and 103:
Figure 6.1: PaciÞc Ocean; streamli
Page 104 and 105:
y 80 70 60 50 40 30 20 10 0 0 20 40
Page 106 and 107:
y 80 70 60 50 40 30 20 10 0 0 20 40
Page 108 and 109:
(a) Top view of a horizontal grid s
Page 110 and 111:
(a) Frame 0 (b) Frame 40 6.2. The B
Page 112 and 113:
(a) Vorticity magnitude (b) Normali
Page 114 and 115:
y 6130 6120 6110 6100 6090 6080 607
Page 116 and 117:
Number of clusters 15 Number of CW
Page 118 and 119:
(a) (b) 6.3. A transitional pipe ß
Page 120 and 121:
(a) Ô (b) (c) (d) É 6.3. A tran
Page 122 and 123:
Figure 6.19: isosurface of high É
Page 124 and 125:
Figure 6.21: Selective streamlines
Page 126 and 127:
Deformable surfaces with scalar cri
Page 128 and 129:
6.4. The Delta-Wing aircraft (a) In
Page 130 and 131:
Chapter 7. Conclusions and future w
Page 132 and 133:
Chapter 7. Conclusions and future w
Page 134 and 135:
Bibliography EKATERINIS, J.A., & SC
Page 136 and 137:
Bibliography MILLER, J.V. 1990. On
Page 138 and 139:
Bibliography SADARJOEN, I.A., VAN W
Page 140 and 141:
Colour Plates 135
Page 142 and 143:
Colour Plates Colour Plate 3: Backw
Page 144 and 145:
Colour Plates Colour Plate 7: Pipe
Page 146 and 147:
Summary this method offers the capa
Page 148 and 149:
Samenvatting methode gebaseerd op k
show all

Chapter 4 Vortex detection - Computer Graphics and Visualization

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?