
Discrete and Computational Geometry
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. - The essential introduction to discrete and computational geometry
- Covers traditional topics as well as new and advanced material
- Features numerous full-color illustrations, exercises, and unsolved problems
- Suitable for sophomores in mathematics, computer science, engineering, or physics
- Rigorous but accessible
- An online solutions manual is available (for teachers only)
More details
Other editions
Additional editions

Persons
Content
- Cover
- Title
- Copyright
- Contents
- Preface
- 1 POLYGONS
- 1.1 Diagonals and Triangulations
- 1.2 Basic Combinatorics
- 1.3 The Art Gallery Theorem
- 1.4 Scissors Congruence in 2D
- 1.5 Scissors Congruence in 3D
- 2 CONVEX HULLS
- 2.1 Convexity
- 2.2 The Incremental Algorithm
- 2.3 Analysis of Algorithms
- 2.4 Gift Wrapping and Graham Scan
- 2.5 Lower Bound
- 2.6 Divide-and-Conquer
- 2.7 Convex Hull in 3D
- 3 TRIANGULATIONS
- 3.1 Basic Constructions
- 3.2 The Flip Graph
- 3.3 The Associahedron
- 3.4 Delaunay Triangulations
- 3.5 Special Triangulations
- 4 VORONOI DIAGRAMS
- 4.1 Voronoi Geometry
- 4.2 Algorithms to Construct the Diagram
- 4.3 Duality and the Delaunay Triangulation
- 4.4 Convex Hull Revisited
- 5 CURVES
- 5.1 Medial Axis
- 5.2 Straight Skeleton
- 5.3 Minkowski Sums
- 5.4 Convolution of Curves
- 5.5 Curve Shortening
- 5.6 The Heat Equation
- 5.7 Curve Reconstruction
- 6 POLYHEDRA
- 6.1 Platonic Solids
- 6.2 Euler's Polyhedral Formula
- 6.3 The Gauss-Bonnet Theorem
- 6.4 Cauchy Rigidity
- 6.5 Shortest Paths
- 6.6 Geodesics
- 7 CONFIGURATION SPACES
- 7.1 Motion Planning
- 7.2 Polygonal Chains
- 7.3 Rulers and Locked Chains
- 7.4 Polygon Spaces
- 7.5 Particle Collisions
- Appendix: Computational Complexity
- Permissions
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Z
System requirements
File format: ePUB
Copy protection: Adobe-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Install the free reader Adobe Digital Editions prior to download (see eBook Help).
- Tablet/smartphone (Android; iOS): Install the free app Adobe Digital Editions or the app PocketBook before downloading (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (not Kindle).
The file format ePub works well for novels and non-fiction books – i.e., „flowing” text without complex layout. On an e-reader or smartphone, line and page breaks automatically adjust to fit the small displays.
This eBook uses Adobe-DRM, a „hard” copy protection. If the necessary requirements are not met, unfortunately you will not be able to open the eBook. You will therefore need to prepare your reading hardware before downloading.
Please note: We strongly recommend that you authorise using your personal Adobe ID after installation of any reading software.
For more information, see our ebook Help page.