Inselberg Parallel Coordinates

Visual Multidimensional Geometry and Its Applications
1. Auflage 2009
ISBN: 978-0-387-68628-8
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 571 Seiten

No short description available.

Autoren/Hrsg.

Inselberg, Alfred

Inhaltsverzeichnis

1;0 Foreword;6
2;0 Contents;8
3;0 Preface;15
3.1;What and Why;15
3.2;Style and Structure of the Book;16
3.3;Course Organization;18
4;0 Acknowledgments;23
5;1 Introduction;27
5.1;1.1 Multidimensional Visualization;27
5.2;1.2;28
6;2 Geometry Background;32
6.1;2.1 Preliminaries;32
6.2;2.2;34
6.3;2.3 ** Finite Geometries;44
6.4;2.4;47
6.5;2.5 The Fundamental Transformations of Projective Geometry;51
6.6;2.6 More on Homogeneous Coordinates;54
6.7;2.7 ** The Linearized Projective Transformations;56
6.8;2.8 ** Coordinate System Rotations;61
6.9;2.9 ** Analytic Proofs;64
6.10;2.10 ** Conics on the Projective Plane;68
6.11;2.11 ** Geometries and Invariants;70
7;3 . FT-1 The Plane with Parallel Coordinates;74
7.1;3.1 The Fundamental Duality;74
7.2;3.2 Transformations under the Duality;82
7.3;3.3 A Preview;86
8;4 Multidimensional Lines;87
8.1;4.1;87
8.2;4.2 Distance and Proximity Properties;112
9;5 Planes, p-Flats, and Hyperplanes;138
9.1;5.1;138
9.2;5.2;147
9.3;5.3;159
9.4;5.4 Hyperplanes and p-Flats in;182
9.5;5.5 ** Construction Algorithms in R4;197
9.6;5.6 Detecting Near Coplanarity;202
9.7;5.7 Representation Mapping, Version II;203
10;6 ** Envelopes;207
10.1;6.1 The Basic Idea;207
10.2;6.2 Formulation;208
10.3;6.3 Necessary and Sufficient Conditions;210
10.4;6.4 Examples: Envelopes of Families of Curves;212
11;7 Curves;217
11.1;7.1;217
11.2;7.2 Duality between Cusps and Inflection Points;221
11.3;7.3;226
11.4;7.4;229
11.5;7.5;238
11.6;7.6;251
11.7;7.7;253
12;8 Proximity of Lines, Planes, and Flats;264
12.1;8.1;264
12.2;8.2 Proximity of Lines and Line Neighborhoods;265
12.3;8.3;272
13;9 Hypersurfaces in;317
13.1;9.1;317
13.2;9.2 Formulation;321
13.3;9.3;324
13.4;9.4;330
13.5;9.5;366
13.6;9.6 ** Approximate Quadric Hypersurfaces;379
13.7;9.7;385
14;10 . FT Data Mining and Other Applications;398
14.1;10.1 Introduction;398
14.2;10.2 Exploratory Data Analysis with;401
14.3;-coords;401
14.4;10.3 Classification;425
14.5;10.4 Visual and Computational Models;435
14.6;10.5 Parallel Coordinates: The Bare Essentials;437
14.7;10.6 Future;444
15;11 Recent Results;447
15.1;11.1 Displaying Several Lines Efficiently;447
15.2;11.2 Separating Point Clusters on Different Planes;461
15.3;11.3 Surface Representation Decomposition and Developable Quadrics;469
15.4;11.4 Network Visualization and Analysis with Parallel Coordinates;478
15.5;References;493
15.6;11.5 To See C2;494
16;12 Solutions to Selected Exercises;507
16.1;12.1 Solutions to Exercises in Chapter 2;507
16.2;12.2 Solutions to Exercises in Chapter 3;527
16.3;12.3 Solutions to Exercises in Chapter 4;532
16.4;12.4 Solutions to Exercises in Chapter 5;538
17;12 Notation and List of Symbols;548
17.1;Alphabetic;548
17.2;Symbols;548
18;12 Bibliography;552
19;12 Index;564