Geometry Algorithm Collections

Collections generally contain surveys and papers giving overviews of selected areas of algorithmic geometry. They do not usually include specialized research papers which can be found in conference proceedings or journals. Rather, an established expert gives an account of current knowledge without the necessity of presenting a new breakthrough; so survey papers can give a more balanced and complete exposition. Often, such collections are referred to as a "Handbook" when the collection of surveys they contain gives comprehensive coverage of a field. There are several excellent Handbooks now available marking the millennium transition.


(2000)		Handbook of Computational Geometry edited by Jorge Urrutia & Jorg-Rudiger Sack
		New: $235.00

	And this handbook (1027 pages + a 48 page index) has 22 chapters by 36 experts. Each chapter is a detailed survey of an area of computational geometry. The book's preface claims that "This handbook presents chapters which survey in detail most of the research available to date in this field", and it comes close to achieving this. However, there are a few glaring omissions, such as not covering triangulation, although there are excellent chapters on "Mesh generation" and "Polygon decomposition". So, it lacks the comprehensiveness of the Goodman & O'Rourke Handbook, but goes into much more detail about implementing algorithms and is more expository. Definitely check them both out.


(2000)		Leda : A Platform for Combinatorial and Geometric Computing by Kurt Mehlhorn & Stefan Naher
		New: Out of Stock List: $120.00 Buy Used from: $149.82

	LEDA is a "Library of Efficient Data types and Algorithms" which is available free to academics, and for a license fee to commercial enterprises. Details about procuring LEDA can be found at their LEDA Web Site. This large (1018 page) book is written by the LEDA developers, well-known and respected computational geometers, who describe the library's environment and algorithms, and give examples of how to use it. The library also includes many graph algorithms, including planar graph drawing. This is a highly regarded recent software product with this book to document its usage (there is also an "HTML Manual" which can be downloaded from the website). Algorithms used are the most efficient and robust ones currently available.


(1999)		Advances in Digital and Computational Geometry by Reinhard Klette, Azriel Rosenfeld, and Fridrich Sloboda (Editors)


	This is an interesting collection of relatively current papers that was a follow-on from the Digital Geometry Day 1997 at Univ. of Auckland, New Zealand. They cover a wide range of topics in both digital and computational geometry, including the topology of patterns, integral geometry, approximation and representation of 3D objects, digitization models, performance analysis of Voronoi algorithms, discrete surface deformations, and more. There are two excellent bibliographies (one for Digital Geometry, and another for Computational Geometry), organized into subject matter areas (e.g., distance and size, point location, rays and lines, polygons, visibility, etc).


(1999)		Algorithms and Theory of Computation Handbook edited by Mikhail Atallah
		New: $94.95

	A recent handbook (1296 pages with 48 chapters) that has amazing coverage of the large field of algorithms in general. Even though the quantity of material related to geometry ("Graph Drawing" = 26 pages; "Computational Geometry" = 60 pages; "Robot Algorithms" = 21 pages) is a small part of this book, it makes up for this in quality. The material is to the point and covers all the main topics. Plus, one gets other chapters about algorithms in many fields which can be applied to geometry algorithm problems (such as, "Basic" and "Dynamic" graph theory = 48 pages, etc). If you only own one Handbook, this may be the one to choose. It has everything.


(1999)		Handbook of Discrete and Combinatorial Mathematics edited by Kenneth Rosen, John Michaels, & Jonathan Gross
		New: $101.88 List: ~~$129.95~~

	This is another huge handbook (1248 pages) which comprehensively covers the field of discrete mathematics. It includes large sections on Graph Theory (12 chapters, 108 pages) and Discrete and Computational Geometry (8 chapters, 92 pages). Implementation details are given for many essential algorithms in these areas. In addition, there are many other chapters in fields that can be brought to bear on geometry algorithm solutions. This is a good general reference to own.


(1998)		Algorithmic Foundations of Geographic Information Systems edited by Marc van Kreveld, Thomas Roos, & Jurg Nievergelt
		New: $69.95 Buy Used from: $49.50

	This is a collection of nine uniformly structured surveys about the use of geometry algorithms and spatial data structures in GIS. Topics covered include: the history of the field, Voronoi methods, terrain modeling and TINs, visualization of TINs, generalization, and robustness of geometric computations. This is an essential reference work for anyone working with GIS's and surface modeling or analysis.


(1997)		Handbook of Discrete and Computational Geometry edited by Jacob Goodman & Joseph O'Rourke
		New: $119.95 Buy Used from: $44.49

	This large handbook (1007 pages) has 52 chapters by 52 experts on 52 different areas, each a comprehensive survey article. Thousands of results - theorems, algorithms, and tables - throughout the volume definitively cover the field, while numerous applications from many different fields demonstrate practical usage. This book does not give algorithm implementation details, but rather describes the performance of known algorithms and then gives references to the literature. It also lists open problems in all areas. This book might be more aptly called a Guidebook to the field.


(1997)		Introduction to Implicit Surfaces edited by Jules Bloomenthal
		New: Out of Stock List: $88.95 Buy Used from: $148.40

	This book has 9 chapters by 7 experts giving an introduction to the fundamental concepts and techniques of implicit surface modeling, rendering, and animating. Topics include surface patches and tilings, ray tracing, blending, animation and special effects of soft deformable objects. This book is a good introduction to existing work in this increasing useful field.


(1995)		Computing in Euclidean Geometry (2nd Edition) edited by Ding-Zhu Du & Frank Hwang
		New: $106.00

	This is a collection of surveys and exploratory articles about recent developments in computational Euclidean geometry. Topics include the history of geometry, Voronoi diagrams, mesh generation, triangulation, randomized algorithms, B-spline patches, topology, and more. The contributors are the best in the field: Hsiang, Chazelle, Eppstein, Fortune, Seidel, and others. This is a highly recommended collection for both the quality and completeness of its papers.