Geometry Algorithm Monographs

These are monographs on specialized topics. They are too specific to be considered a survey, and are not suitable for a general course for more than a few students. However, they present more in-depth discussions and exposition than is appropriate for a journal article. Usually, they give a definitive treatment of a specialized subfield, and are directed at experts rather than novices.


(2001)		Geometry and Topology for Mesh Generation by Herbert Edelsbrunner
		New: Out of Stock List: $49.99 Buy Used from: $123.75

	Finally, there is a clearly written book, by a highly-regarded expert, on the difficult topic of Delaunay triangulation and tetrahedralization with application to 2D and 3D meshes. Although small in size, it packs a huge amount of information, covering both theory and algorithms. The final section (37 pages) lists and discusses 23 significant open problems. This is a book for both the serious researcher as well as the interested spectator and practitioner. Highly recommended.


(2001)		Computational Line Geometry by Helmut Pottmann & Johannes Wallner
		New: $90.20 List: ~~$113.00~~ Buy Used from: $64.00

	This is an advanced book about computing in differential geometry involving linear spaces, projective spaces, algebraic geometry, ruled and developable surfaces. There are no algorithms per se, but there is a lot of computing machinery, mostly oriented to the mathematician. Notably, the material is explained in a very accessible and clear manner. There are interesting treatments of Bezier and B-spline curves, Plucker coordinates, the Grassmann algebra of forms. and more.


(2000)		Spatial Tessellations : Applications of Voronoi Diagrams by Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Chiu, & Michiko Okabe
		New: $172.00 List: ~~$220.00~~ Buy Used from: $154.95

	This book covers the theory, algorithms, and a huge range of applications (in over a dozen fields) of spatial tessellations, including Voronoi diagrams and Delaunay tessellations.


(2000)		An Introduction to NURBS: With Historical Perspective by David Rogers
		New: $57.56 List: ~~$71.95~~ Buy Used from: $49.94

	A comprehensive introduction to the mathematics of NURBS with pseudo-code for all important algorithms (C-code for worked examples is online). In each chapter, there are contributed historical perspectives of the current state of the art written by prominent researchers the field. The book gives thorough coverage of Bezier, B-spline, and rational B-spline parametric curves and surfaces, culminating in "A Fast Rational B-spline Surface Algorithm".


(2000)		The Discrepancy Method : Randomness and Complexity by Bernard Chazelle
		New: $70.30 List: ~~$101.00~~ Buy Used from: $44.58

	This is a theoretical book by the world's foremost computational geometer, and is concerned with the relationship between the complexity of geometry algorithms and computational randomness. Some topics it covers are: communication complexity, pseudo-randomness, Markov chains, derandomization, convex hulls and Voronoi diagrams, linear programming, geometric sampling, minimum spanning trees, circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained.


(1999)		NURBS : From Projective Geometry to Practical Use by Gerald Farin
		New: $49.00

	This book explains how to use NURBS surface patches to create complicated computer graphics models. As with Farin's other books, the material is clearly and cleanly presented.


(1999)		Curves and Surfaces in Geometric Design: Theory and Algorithms by Jean Gallier
		New: Out of Stock List: $96.95 Buy Used from: $122.45

	This book gives both a theoretical understanding of polynomial curves and surfaces, as well as an effective approach for using and implementing them in geometric modeling applications.


(1998)		Graph Drawing : Algorithms for the Visualization of Graphs by Giuseppe Di Battista, Peter Eades, Roberto Tamassia, & Ionnis Tollis
		New: $73.60 List: ~~$92.00~~ Buy Used from: $55.20

	This book presents basic algorithmic techniques for automatically constructing 2D drawings of graphs of objects and the connections between them. It presents both divide-and-conquer and incremental algorithms, and considers flow, orthogonal, and layered drawings.


(1997)		The NURBS Book by Les Piegl & W. Tiller (Contributor)
		New: $61.40 List: ~~$74.95~~ Buy Used from: $42.95

	This book is a very complete mathematically oriented treatment of B-splines. It includes curve and surface algorithms, and state-of-the-art geometry tools with detailed code and computational tricks. It is clearly written with good explanations and many examples. This is a highly recommended introduction to NURBS.


(1996)		Geometrical Methods in Robotics by J. M. Selig
		New: Out of Stock List: $66.95 Buy Used from: $53.97

	This is a high level mathematical approach to robot kinematics using differential geometry. There are no algorithms presented or discussed. Nevertheless, it may be of some help to an expert, but is not an introductory text.


(1995)		Randomized Algorithms by Rajeev Motwani & Prakhabar Raghavan
		New: $55.20 List: ~~$69.00~~ Buy Used from: $34.00




(1995)		Davenport-Schinzel Sequences and Their Geometric Applications by Micha Sharir & Pankaj Agarwal
		New: $43.89 List: ~~$95.00~~

	These sequences are now a fundamental tool for solving many problems in computational geometry. This book studies them in detail, and gives applications to robot motion planning, computer graphics, and pattern matching.


(1993)		Curves and Surfaces for Computer Aided Geometric Design by Gerald Farin
		New: Out of Stock List: $68.95 Buy Used from: $191.01

	An outstanding text emphasizing Bezier curves and patches which are "the most stable among all polynomial bases currently used in CAD systems". It also covers B-splines in detail, as well as some other patches such as the Coons patch. There is a historical introduction, a refresher of vector geometry, and two excellent chapters on differential geometry, I and II, well-placed in the middle of the book. This book is clearly written with in-depth and accurate explanations of the mathematics and algorithms. If you want to understand CAGD, or even just applied differential geometry of curves and surfaces, this is the book for you. We highly recommend it as an intermediate level text. It comes with a disk containing "C" code implementations of the methods presented.


(1993)		Three-Dimensional Computer Vision : A Geometric Viewpoint by Oliver Faugeras
		New: $83.50 List: ~~$100.00~~ Buy Used from: $25.00

	A thorough and mathematically rigorous exposition of the problems and techniques related to three-dimensional (stereo) computer vision and motion. There is emphasis on using geometry in problem solving, with examples from navigation and object recognition.


(1991)		Intersection and Decomposition Algorithms for Planar Arrangements by Pankaj Agarwal
		New: $95.00 Buy Used from: $7.95

	This book presents a study of various problems related to arrangements of lines, segments, or curves in the plane. Topics include: Davenport-Schinzel sequences, intersection detection, plane partitioning, and spanning trees.


(1987)		Art Gallery Theorems and Algorithms by Joseph O'Rourke
		New: Out of Stock List: $60.00

	The "art gallery problem" is to determine how to position guards to maintain visibility of all objects in the gallery (given by its floor plan). Abstracting the problem, this book studies the visibility of geometrical shapes and their surfaces. It discusses the interior visibility of polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. As well as descriptions of algorithms, many open problems and conjectures are presented.


(1983)		Linear Programming by Chvatal
		New: $75.95 Buy Used from: $41.83

	This is a classic masterpiece, and still one of the best books on linear programming. It is an excellent clearly written introduction to these types of algorithms.