Projective geometry is the geometry of vision, and this book introduces students to this beautiful subject from an analytic perspective, emphasising its close relationship with linear algebra and the central role of symmetry. Starting with elementary and familiar geometry over real numbers, readers will soon build upon that knowledge via geometric pathways and journey on to deep and interesting corners of the subject. Through a projective approach to geometry, readers will discover connections between seemingly distant (and ancient) results in Euclidean geometry. By mixing recent results from the past 100 years with the history of the field, this text is one of the most comprehensive surveys of the subject and an invaluable reference for undergraduate and beginning graduate students learning classic geometry, as well as young researchers in computer graphics. Students will also appreciate the worked examples and diagrams throughout.
Author(s): John Bamberg, Tim Penttila
Edition: 1
Publisher: Cambridge University Press
Year: 2023
Language: English
Commentary: Publisher PDF
Pages: xii, 462
City: Cambridge, United Kingdom
Tags: Analytic Projective Geometry; Mathematics; Computer Science; Computer Graphics; Image Processing; Robotics; Geometry; Topology
Frontmatter
pp i-vi
Contents
pp vii-x
Preface
pp xi-xii
Part I - The Real Projective Plane
pp 1-2
1 - Fundamental Aspects of the Real Projective Plane
pp 3-11
2 - Collineations
pp 12-30
3 - Polarities and Conics
pp 31-42
4 - Cross-Ratio
pp 43-82
5 - The Group of the Conic
pp 83-99
6 - Involution
pp 100-162
7 - Real Affine Plane Geometry from a Projective Perspective
pp 163-183
8 - Euclidean Plane Geometry from a Projective Perspective
pp 184-240
9 - Transformation Geometry: Klein’s Point of View
pp 241-245
10 - The Power of Projective Thinking
pp 246-287
11 - From Perspective to Projective
pp 288-316
12 - Remarks on the History of Projective Geometry
pp 317-320
Part II - Real Projective 3-Space
pp 321-322
13 - Fundamental Aspects of Real Projective Space
pp 323-337
14 - Triangles and Tetrahedra
pp 338-347
15 - Reguli and Quadrics
pp 348-367
16 - Line Geometry
pp 368-387
17 - Projections
pp 388-396
18 - A Glance at Inversive Geometry
pp 397-404
Part III - Higher Dimensions
pp 405-406
19 - Generalising to Higher Dimensions
pp 407-420
20 - The Klein Quadric and the Veronese Surface
pp 421-433
Appendix: Group Actions
pp 434-435
References
pp 436-456
Index
pp 457-462
