This book is an interactive introduction to some of the fundamental algorithms of computational geometry.
In a conventional paper-based textbook these algorithms are either presented as narrative, in pseudo code or in a language such as C or Java. Often (but not always) there is a separate code base that the reader can download and use. However, in this book, the code base, which is in the Wolfram Language, is integrated into the text, and is fully executable. We are no longer limited to a static description of algorithms, we present functioning, executing code that implements and demonstrates these algorithms.
There is nothing quite like seeing an algorithm in action. We have found that a good interactive demonstration can replace an extraordinary amount of text. Furthermore, whereas a textual (and to a lesser extent, pseudo code) description of an algorithm may be subject to the ambiguity of natural language, the demonstration is unambiguous because it is the algorithm in action.
This book is delivered as an interactive CDF (Computable Document Format) file that you can view in the free CDF Player available from Wolfram, or, you can open it in Mathematica. All the code is executable, and, if you have access to Mathematica, we encourage you to play about with it, either by working on a copy of this text, or by cutting and pasting snippets into a new Mathematica Notebook. In fact, to get the most from this text, you really should have a copy of Mathematica!
Table of contents
- Introduction
- Chapter 1 - points and lines
- Chapter 2 - polygonal chains
- Chapter 3 - triangles and the relationship of points to lines
- Chapter 4 - polygons
- Chapter 5 - intersections
- Chapter 6 - convex hulls
- Chapter 7 - polygon triangulations
- Chapter 8 - point set triangulation and dual graph
- Chapter 9 - Delaunay triangulation
- Chapter 10 - Voronoi diagrams
- Summary
- Bibliography