Parallel Coordinates (eBook)

Visual Multidimensional Geometry and Its Applications

Alfred Inselberg (Autor)

eBook Download: PDF

2009 | 1. Auflage
571 Seiten
Springer New York (Verlag)
978-0-387-68628-8 (ISBN)

Infos

No short description available.

---

The breakthrough idea of parallel coordinates has enchanted many people with its cleverness and power. Al Inselberg, the source of that cleverness and power, ?nally shares the depth and breadth of his invention in this historically important book. I've been waiting impatiently for this exposition since I was captivated by Inselberg'slectureattheUniversityofMarylandin1979.Hehadalreadyunderstood the potential parallel coordinates has for generating insights into high-dimensional analysis and information visualization. In the following decades he polished the arguments, built effective software, and demonstrated value in important appli- tions. Nowabroadcommunityofreaderscanbene?tfromhisinsightsandeffective presentation. I believe that Inselberg's parallel coordinates is a transformational ideal that ' matches the importance of Rene Descartes' (1596-1650) invention of Cartesian coordinates. Just as Cartesian coordinates help us understand 2D and 3D geometry, parallel coordinates offer fresh ways of thinking about and proving theorems in higher-dimensional geometries. At the same time they will lead to more powerful tools for solving practical problems in a wide variety of applications. It is rare to encounter such a mind-shattering idea with such historic importance. While Inselberg's insight and exposition opens the door to many discoveries, there is much work to be done for generations of mathematicians, computer sci- tists, programmers, and domain experts who will need to build on these innovative ideas.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 15.8.2009
• Sprache: englisch
• Themenwelt: Informatik ► Software Entwicklung ► User Interfaces (HCI)
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Technik
• ISBN-10: 0-387-68628-2 / 0387686282
• ISBN-13: 978-0-387-68628-8 / 9780387686288