Preface |
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ix | |
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1 | (10) |
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1 | (2) |
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1.2 Historical Development and Progress in Visual Science |
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3 | (4) |
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1.3 Scientific Visualization Philosophy, Techniques and Challenges |
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7 | (4) |
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2 Field Descriptions and Kinematics |
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11 | (52) |
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2.1 Lagrangian/Eulerian Description and Transformation |
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11 | (4) |
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2.2 Curvilinear Coordinates |
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15 | (34) |
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24 | (5) |
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2.2.2 Streamline (Flux Line) Coordinates |
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29 | (14) |
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2.2.3 Potential-Stream Function Coordinates |
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43 | (6) |
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2.3 Field Kinematics and Visual Attributes |
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49 | (14) |
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2.3.1 Field Line Trajectory |
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49 | (1) |
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2.3.2 Field Line Integral Curves |
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50 | (4) |
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2.3.3 Field Lines, Material Lines and Path Lines |
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54 | (2) |
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2.3.4 Streamlines (Flux Lines) |
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56 | (7) |
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3 Field Model, Representation and Visualization |
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63 | (34) |
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3.1 Field Models and Concepts |
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63 | (2) |
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3.2 Scalar Fields and Representation |
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65 | (3) |
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3.3 Vector Fields and Representation |
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68 | (1) |
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3.4 Vector Icons and Classifications |
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69 | (2) |
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3.4.1 Classification Based on Domain Configurations |
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70 | (1) |
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3.4.2 Classification Based on Information Levels |
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70 | (1) |
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3.4.3 Classification Based on Topological Skeleton |
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71 | (1) |
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71 | (3) |
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74 | (3) |
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3.7 Vector Field Specification |
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77 | (2) |
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3.7.1 Helmholtz's Theorem |
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77 | (2) |
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3.8 Tensor Contraction and Transport Process Visualization |
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79 | (6) |
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3.8.1 Mechanical Energy Function and Heatfunction |
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80 | (4) |
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3.8.2 Strain Energy Trajectory and Strain Function |
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84 | (1) |
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85 | (12) |
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4 Complex Analysis and Complex Potentials |
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97 | (30) |
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4.1 Complex Variables/Functions and Applications |
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97 | (3) |
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4.2 Complex Analysis and Cauchy-Riemann Equation |
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100 | (1) |
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4.3 Differentiation of Complex Function |
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101 | (3) |
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4.4 Integration of Complex Functions |
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104 | (3) |
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4.5 Visualization of Complex Potentials |
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107 | (7) |
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107 | (1) |
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4.5.2 Method of Curvilinear Squares |
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108 | (3) |
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4.5.3 Transfer Characteristics and Field Property Evaluation |
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111 | (3) |
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4.6 Example 4.1a Visualization of Heat and Fluid Transport in a Corner |
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114 | (13) |
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5 Field Mapping and Applications |
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127 | (72) |
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127 | (2) |
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5.2 Mapping of Euclidean Geometry |
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129 | (4) |
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129 | (2) |
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131 | (1) |
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132 | (1) |
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133 | (2) |
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134 | (1) |
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5.4 Mapping with Complex Functions |
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135 | (2) |
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5.5 Conformal Mapping and Applications |
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137 | (10) |
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5.6 Hodograph Method and Mapping |
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147 | (2) |
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5.6.1 Conjugate Hodograph |
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148 | (1) |
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149 | (1) |
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5.7 Hodograph Representations and Applications |
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149 | (34) |
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5.7.1 Straight Boundaries |
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156 | (2) |
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158 | (2) |
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5.7.3 Special Field Patterns |
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160 | (3) |
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5.7.4 Projectile Trajectory in Constant Force Fields |
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163 | (6) |
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5.7.5 Motion Trajectory in Central Force Fields |
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169 | (10) |
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5.7.6 Trajectory of Charged Particles in Uniform Magnetic Fields |
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179 | (4) |
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5.8 Example 4.1b Mapping of Field Patterns and Image Warping |
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183 | (16) |
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6 Tensor Representation, Contraction and Visualization |
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199 | (50) |
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199 | (1) |
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6.2 Development of Tensor Visualization Techniques |
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200 | (1) |
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200 | (1) |
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6.2.2 Tensor Field Line Trajectories (Lines of Principal Stress) |
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200 | (1) |
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201 | (1) |
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201 | (1) |
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6.2.5 Stress Trajectories |
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201 | (1) |
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201 | (1) |
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201 | (1) |
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6.3 Tensor Description and Representation |
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201 | (3) |
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6.3.1 Tensor Icons and Classification |
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204 | (1) |
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6.4 Tensor Decomposition and Tensor Rank Reduction |
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204 | (10) |
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6.4.1 Strain Tensor and Stress Tensor |
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206 | (1) |
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207 | (1) |
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6.4.3 Rate of Strain Tensor and Viscous Stress Tensor |
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208 | (2) |
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210 | (3) |
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6.4.5 Tensor Contractions: Tensor Vector on a Reference Plane |
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213 | (1) |
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6.4.6 Tensor Contractions: Tensor Vector at a Point |
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214 | (1) |
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6.5 Visualization of Symmetric Tensors |
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214 | (14) |
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214 | (3) |
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6.5.2 Tensor Transformation |
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217 | (1) |
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6.5.3 Principal States and Eigenanalysis |
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217 | (10) |
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6.5.4 Hybrid Method of Tensor Visualization |
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227 | (1) |
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6.6 Visualization of Antisymmetric Tensors |
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228 | (14) |
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6.6.1 Vorticity Concepts and Dynamics |
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228 | (4) |
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232 | (5) |
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237 | (3) |
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6.6.4 Vortices Transport and Vorticity Function |
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240 | (2) |
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6.7 Example: 4.1c Convective Momentum Flux Tensor Visualization |
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242 | (7) |
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7 Critical Point Topology, Classification and Visualization |
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249 | (24) |
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249 | (2) |
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7.2 Complex Analysis of Critical Point |
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251 | (6) |
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7.3 Critical Point Theory and Classification |
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257 | (6) |
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7.3.1 Symmetric Tensor: [ V] = [ V]T; Im1 = Im2 = 0 |
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261 | (1) |
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7.3.2 Antisymmetric Tensor: ii = 0, i = j; ij = -ji, i j |
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262 | (1) |
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262 | (1) |
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7.4 Example 4.1d Critical Point Topology |
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263 | (2) |
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7.5 Singular Point Visualization and Mapping |
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265 | (1) |
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7.6 Example 7.1 Mapping of a Point Source |
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266 | (7) |
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8 Engineering Application Examples |
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273 | (92) |
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8.1 Example 8.1: Torsion of a Square Beam |
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273 | (29) |
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8.2 Example 8.2: Bending of a Cantilever Beam Subject to a Point Load |
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302 | (21) |
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8.3 Example 8.3: Squeezing Flow and Vorticity Transport |
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323 | (22) |
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8.4 Example 8.4: Groundwater Flows in an Anisotropic Porous Medium |
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345 | (20) |
References |
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365 | (4) |
Index |
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369 | |