Oriented Projective Geometry. A Framework for Geometric Computations

✍ Scribed by Jorge Stolfi (Auth.)

• Publisher: Elsevier Inc, Academic Press
• Year: 1991
• Tongue: English
• Leaves: 233
• Category: Library

✦ Synopsis

Intended for computer graphics researchers and programmers, and mathematicians working in computational geometry. This book describes oriented projective geometry, a geometric model that combines the elegance and efficiency of classical projective geometry with the consistent handling of oriented lines and planes, signed angles, line segments, convex sets, and many other fundamental geometric computing concepts that classical theory does not support. The aim of this book is to assemble a consistent, practical and effective set of tools for computational geometry that can be used by graphics programmers in their everyday work. In keeping with this goal, formal derivations are kept to a minimum, and many definitions and theorems are illustrated with explicit examples in one, two, and three dimensions

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
Introduction, Pages 1-2
Chapter 1 - Projective geometry, Pages 3-12
Chapter 2 - Oriented projective spaces, Pages 13-18
Chapter 3 - Flats, Pages 19-27
Chapter 4 - Simplices and orientation, Pages 29-38
Chapter 5 - The join operation, Pages 39-45
Chapter 6 - The meet operation, Pages 47-58
Chapter 7 - Relative orientation, Pages 59-66
Chapter 8 - Projective maps, Pages 67-76
Chapter 9 - General two-sided spaces, Pages 77-82
Chapter 10 - Duality, Pages 83-93
Chapter 11 - Generalized projective maps, Pages 95-105
Chapter 12 - Projective frames, Pages 107-122
Chapter 13 - Cross ratio, Pages 123-130
Chapter 14 - Convexity, Pages 131-150
Chapter 15 - Affine geometry, Pages 151-165
Chapter 16 - Vector algebra, Pages 167-172
Chapter 17 - Euclidean geometry on the two-sided plane, Pages 173-190
Chapter 18 - Representing flats by simplices, Pages 191-196
Chapter 19 - Plücker coordinates, Pages 197-205
Chapter 20 - Formulas for Plücker coordinates, Pages 207-222
References, Pages 223-224
List of symbols, Pages 225-226
Index, Pages 227-237