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Preface | p. vii |
Combinatorial Figures | p. 1 |
Drawing figures | p. 2 |
Modeling figures | p. 4 |
The circuits of a figure | p. 12 |
Combinatorial Geometries | p. 15 |
The definition of a combinatorial geometry | p. 15 |
Lines and planes of a combinatorial geometry | p. 17 |
Two families of combinatorial geometries | p. 24 |
Sketches of planar geometries and figures | p. 28 |
Models of some combinatorial cubes | p. 32 |
Subgeometries of a combinatorial geometry | p. 35 |
Isomorphic combinatorial geometries | p. 36 |
Planar Geometries and Projective Planes | p. 41 |
The intersection of coplanar lines | p. 42 |
Projective planes | p. 43 |
Subgeometries of a projective plane | p. 55 |
An extended Euclidean plane | p. 57 |
Pencil and roller constructions | p. 63 |
Coordinatizing an extended Euclidean plane | p. 65 |
Sylvester's Theorem and the Fano plane | p. 69 |
Non-Planar Geometries and Projective Spaces | p. 71 |
Projective spaces | p. 71 |
Subgeometries of a projective space | p. 78 |
Desargues' Theorem and projective spaces | p. 79 |
Extended Euclidean space | p. 82 |
Coordinatizing extended Euclidean space | p. 91 |
Perpendicular lines and planes | p. 97 |
Pythagoras' Theorem, length and angle | p. 99 |
The existence of a tetrahedron | p. 102 |
Perspective Drawings | p. 105 |
The definition and basic properties of a perspective drawing | p. 106 |
Perspective drawings in a combinatorial geometry | p. 112 |
Practical perspective drawing methods | p. 113 |
Vanishing points | p. 116 |
Perspective drawings of a box | p. 122 |
Perspective rendition from an ideal viewpoint | p. 129 |
Binocular Vision and Single Image Stereograms | p. 133 |
Binocular vision | p. 133 |
Binocular vision and random-dot stereograms | p. 137 |
Single-image stereograms | p. 140 |
Scene Analysis | p. 143 |
Perspective drawings of intersections of planes | p. 144 |
Scenes and other planar figures | p. 149 |
The existence of boxes | p. 152 |
Completing a partial scene | p. 158 |
Two problems | p. 162 |
Distortion and Anamorphic Art | p. 167 |
Viewing perspective drawings | p. 167 |
Anamorphic art | p. 169 |
Distortion in 3-point perspective drawings | p. 171 |
Distortion in 2-point perspective drawings | p. 174 |
Distortion in 1-point perspective drawings | p. 176 |
Distortion in affine projections | p. 179 |
Planar Bar-And-Joint Mechanisms | p. 183 |
Bar-and-joint models | p. 184 |
Four-bar linkages | p. 186 |
Rocking and rotation in 4-bar linkages | p. 189 |
Coupler curves | p. 196 |
Parallelogram and kite linkages | p. 200 |
Plagiographs | p. 202 |
Cognate linkages | p. 204 |
Approximate and exact linear motion | p. 209 |
Non-Planar Hinged-Panel-Mechanisms | p. 213 |
Hinged-panel models | p. 213 |
Four-panel cycles | p. 222 |
Panel cycles of at least five panels | p. 225 |
Polyhedral models | p. 234 |
Graphs, Models and Geometries | p. 239 |
The definition of a graph | p. 239 |
Connected graphs and acyclic graphs | p. 242 |
The rigidity of a one-story building | p. 245 |
Hinge graphs and developments | p. 247 |
Graphs that are also geometries | p. 252 |
Spherical Polyhedra | p. 255 |
The definition of a polyhedron | p. 255 |
Planar graphs and three-connected graphs | p. 258 |
The definition of a spherical polyhedron | p. 261 |
Vertices, edges, and faces of a spherical polyhedron | p. 262 |
The existence of spherical polyhedra | p. 265 |
Dürer's melancholy octahedron | p. 270 |
Scene Analysis and Spherical Polyhedra | p. 275 |
Perspective drawings of a spherical polyhedron | p. 275 |
Some applications of the theorem | p. 279 |
Perspective drawings of a wider class of unions of polygonal regions | p. 285 |
. Matroids | p. 287 |
The definition of a matroid | p. 287 |
Geometries, graphs, and matroids | p. 290 |
Bases of a matroid | p. 294 |
The rank function of a matroid | p. 296 |
Isomorphism and representable matroids | p. 299 |
Projective and affine geometry | p. 302 |
Dual matroids | p. 305 |
Restrictions and contractions of a matroid | p. 307 |
Minors of a matroid | p. 310 |
Paving matroids | p. 315 |
Bibliography | p. 317 |
Index | p. 321 |
Table of Contents provided by Ingram. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.