Parallel Coordinates (eBook)

0 Foreword 6
0 Contents 8
0 Preface 15
What and Why 15
Style and Structure of the Book 16
Course Organization 18
0 Acknowledgments 23
1 Introduction 27
1.1 Multidimensional Visualization 27
1.2 28
2 Geometry Background 32
2.1 Preliminaries 32
2.2 34
2.3 ** Finite Geometries 44
2.4 47
2.5 The Fundamental Transformations of Projective Geometry 51
2.6 More on Homogeneous Coordinates 54
2.7 ** The Linearized Projective Transformations 56
2.8 ** Coordinate System Rotations 61
2.9 ** Analytic Proofs 64
2.10 ** Conics on the Projective Plane 68
2.11 ** Geometries and Invariants 70
3 . FT-1 The Plane with Parallel Coordinates 74
3.1 The Fundamental Duality 74
3.2 Transformations under the Duality 82
3.3 A Preview 86
4 Multidimensional Lines 87
4.1 87
4.2 Distance and Proximity Properties 112
5 Planes, p-Flats, and Hyperplanes 138
5.1 138
5.2 147
5.3 159
5.4 Hyperplanes and p-Flats in 182
5.5 ** Construction Algorithms in R4 197
5.6 Detecting Near Coplanarity 202
5.7 Representation Mapping, Version II 203
6 ** Envelopes 207
6.1 The Basic Idea 207
6.2 Formulation 208
6.3 Necessary and Sufficient Conditions 210
6.4 Examples: Envelopes of Families of Curves 212
7 Curves 217
7.1 217
7.2 Duality between Cusps and Inflection Points 221
7.3 226
7.4 229
7.5 238
7.6 251
7.7 253
8 Proximity of Lines, Planes, and Flats 264
8.1 264
8.2 Proximity of Lines and Line Neighborhoods 265
8.3 272
9 Hypersurfaces in 317
9.1 317
9.2 Formulation 321
9.3 324
9.4 330
9.5 366
9.6 ** Approximate Quadric Hypersurfaces 379
9.7 385
10 . FT Data Mining and Other Applications 398
10.1 Introduction 398
10.2 Exploratory Data Analysis with 401
-coords 401
10.3 Classification 425
10.4 Visual and Computational Models 435
10.5 Parallel Coordinates: The Bare Essentials 437
10.6 Future 444
11 Recent Results 447
11.1 Displaying Several Lines Efficiently 447
11.2 Separating Point Clusters on Different Planes 461
11.3 Surface Representation Decomposition and Developable Quadrics 469
11.4 Network Visualization and Analysis with Parallel Coordinates 478
References 493
11.5 To See C2 494
12 Solutions to Selected Exercises 507
12.1 Solutions to Exercises in Chapter 2 507
12.2 Solutions to Exercises in Chapter 3 527
12.3 Solutions to Exercises in Chapter 4 532
12.4 Solutions to Exercises in Chapter 5 538
12 Notation and List of Symbols 548
Alphabetic 548
Symbols 548
12 Bibliography 552
12 Index 564