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Computer Graphics is one of the main areas of application for computational geometry algorithms.   This is most evident in entertainment animation for both movies and computer games.  The efficiency and accuracy of the geometry algorithms is important in determining both the level of detail and realism of animations.  There are also many other important areas of application, such as scientific and medical imaging.  Here are some books that show you how to do it.
(2003) Tricks of the 3D Game Programming Gurus - Advanced 3D Graphics
by Andre LaMothe
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This large (1728 page) book explains in detail how to design and implement a 3D game with C++ code for a sample spaceflight shooter game. It clearly explains the geometric concepts math, and algorithms that underlie realistic real time games. Topics include wireframe modeling, shading, texture, shadows, visibility, animation, and collision detection. This book gives you everything you need to successfully develop 3D games.

(2002) Level of Detail for 3D Graphics
by David Luebke, Martin Reddy, Jonathan Cohen, Amitabh Varshney, Benjamin Watson, and Robert Huebner
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This book explores the trade-offs between realism and efficiency.  Both beautifully detailed graphics as well as smooth animation are important in an application, but they are in conflict.  This book shows how to adjust the level of detail to match the performance needs of an application.  Topics include mesh simplification, human perception, and visual fidelity measurement. It also covers the important area of detail in terrain visualization. These topics are usually not well covered elsewhere, making this an important and useful text. There is a book web site with extra supporting material and software.

(2002) Real-Time Shader Programming
by Ron Fosner
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This introductory book covers the mathematics of lighting and shading, and implementation in DirectX.

(2002) Real-Time Shading
Edited by Marc Olano, John Hart, Wolfgang Heidrich, & Michael McCool
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This introductory book covers the fundamentals of lighting, shading, and texturing, as well as the real time algorithms for implementing them.

(2002) Geometric Tools for Computer Graphics
by Philip Schneider & David Eberly
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A massive encyclopedia (1056 pages) of basic geometry algorithms (including sample code). This book covers 2D and 3D, with special treatment for all the special case algorithms to compute distance, approximation, containment, decomposition, intersection, separation, boolean operations, etc for linear and quadratic geometric objects.  This is an essential reference for you to own, and will save you countless hours of time. Very reasonably priced for the quantity of material it contains.  David Eberly maintains a web site, Magic Software, with material and source code  related to the book.

(2002) Real-Time Rendering (2nd Edition)
by Tomas Moller & Eric Haines
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A practitioner's bible with a large number of efficient computational techniques for computer graphics applications.  Included are intersection and collision test methods, lighting and shading, texturing, special effects, speed up techniques, polygon methods, pipeline optimization, and more.  This is a valuable reference work to own.  They also have a great web site on Real-Time Rendering Resources with many links to sites concerning the wide range of topics covered in the book.

(2002) cover Interactive Computer Graphics: A Top-Down Approach with OpenGL (3rd Edition)
by Edward Angel
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An excellent book for the beginning graphics programmer.

(2002) Handbook of Geometric Programming Using Open Geometry GL
by Georg Glaeser & H
ans-Peter Schrocker
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(1999) cover Open Geometry : OpenGL + Advanced Geometry
by Georg Glaeser & Hellmuth Stachel
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These books are about geometry algorithms, and use OpenGL for programming.  They also have CDs with each book that have all code including the "Open Geometry GL" C++ library (with source code) in the second book. This library is mathematically quite powerful, and works with the popular OpenGL graphics language.  There is good coverage of 2D and 3D geometric modeling of various interesting curves, polygons, surfaces, and polyhedrons.  If you are a programmer writing geometry-oriented code, these are important references to own, and the Open Geometry GL library is a powerful toolkit. There is an Open Geometry web site related to the book.

(2002) Game Programming Gems 3
edited by Dante Treglia & Mark Deloura
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(2001) Game Programming Gems 2
edited by Mark Deloura
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The successor to the Graphics Gems legacy, this new series collects together the tricks of the game programming gurus.  There are sections on programming techniques, math, AI, polygon techniques, and special effects.  There are contributions from over 100 different experts.  If you do graphics and geometric programming, these are great sources for creative ideas.

(2002) 3D Math Primer for Graphics and Game Development
by Fletcher Dunn & Ian Parberry
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This book covers fundamental 3D math concepts used in computer game development and programming.  It includes working C++ class implementations.

(2001) 3D Game Engine Design : Practical Real-Time Computer Graphics
by David Eberly
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An awesome collection of techniques for computer graphics modeling and animation with an emphasis on geometric algorithms and computations.  This book has a polished mathematical orientation with a focus on efficient implementation as software algorithms, hence the "real-time".  This highly recommended book is a necessary reference for advanced animated graphics programmers.  Topics include: geometric methods, the graphics pipeline, intersection and collision detection, curves and surfaces, animation, terrain rendering, and special effects.  The book includes a CD with source code for the huge library of routines covered in the book.  The author's web site is Magic Software.

(2001) Mathematics for 3D Game Programming & Computer Graphics
by Eric Lengyel
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This book covers the math concepts needed to develop a 3D game display engine using OpenGL.  This is an excellent and concise book that thoroughly covers the basics.  Good as an introduction to 3D graphics programming.

(2001) Practical Algorithms for 3D Computer Graphics
by Stuart Ferguson
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This book presents many key algorithms of 3D computer graphics software, particularly computer games. It explains rendering, animation techniques, polygonal modeling, and much more.

(2000) cover Realistic Ray Tracing
by Peter Shirley
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This book gives the nuts-and-bolts of writing ray tracing programs, with many C++ code segments.

(2000) Game Programming Gems
edited by Mark Deloura
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The successor to the Graphics Gems legacy, this new series collects together the tricks of the game programming gurus.  There are sections on programming techniques, math, AI, polygon techniques, and special effects.  There are contributions from over 100 different experts.  If you do graphics and geometric programming, these are great sources of creative ideas.

(2000) Computer Graphics Using OpenGL
by Francis Hill
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Highly practical -- and exceptionally accessible -- this book combines the principles and major techniques in computer graphics with state-of-the-art examples. Uniquely thorough and integrated in approach, it carefully presents each concept, explains the underlying mathematics and why it is important, shows how to translate the math into program code, and shows the result.  Uses OpenGL and C++ throughout.

(1999) cover OpenGL(R) Programming Guide: The Official Guide ... (3rd Edition)
by Mason Woo, Jackie Neider, Tom Davis, Dave Schreiner, and the OpenGL Architecture Review Board
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If you want to learn OpenGL, this is the book for you.

(1999) cover 3D Computer Graphics (3rd Edition)
by Alan Watt
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A first rate advanced text.

(1999) Mathematics for Computer Graphics Applications
by Michael Mortenson
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This book is an introduction to the mathematical  foundations of computer graphics applications, including CAD/CAM, geometric modeling, and scientific visualization.  It is clearly written and easily understood by a beginner.  Chapter topics include: linear algebra basics, symmetry and groups, topology, points & lines & planes, polygons & polyhedra, solid geometry, curves & surfaces, and graphics display transformations.  It is very elementary, but brings all the basics together in one book.

(1998) The Visualization Toolkit (2nd Edition)
by William Schroeder, Kenneth Martin, and Bill Lorensen
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This book is subtitled: "An Object-Oriented Approach to 3D Graphics".

(1998) The Geometry Toolbox for Graphics and Modeling
by Gerald Farin & Dianne Hansford
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A textbook for a one-semester undergraduate course introducing linear algebra from a geometric perspective and geometry from the perspective of algorithms. The theoretical ceiling is kept low, often substituting examples and images for exact proofs.  The book web page is: The Geometry Toolbox.

(1997) cover Geometric Modeling 
by Michael Mortenson
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This book describes and compares all the important mathematical methods for modeling curves, surfaces, and solids, and shows how to transform and assemble these elements into complex models.  It is an introductory text, and lacks depth in some areas, but the style is easy to read and understand.  Topics include:  Hermite, Bezier, and B-Spline curves and surfaces; solids; transformations; and complex model construction.

(1996) cover Computer Graphics: Principles and Practice (2nd Edition in C)
by James Foley, Andries van Dam, Steven Feiner, & John Hughes
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This is the bible of Computer Graphics (1175 pages) covering almost all of the field.  It contains many geometric algorithms that pertain to the rendering of 2D and 3D graphics displays.  Although this is a first rate textbook, it can also be regarded as a collection or survey.  It is an essential affordable reference book.

(1995) cover Graphics Gems V
edited by Alan Paeth
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This book is part of the excellent Graphics Gems I-V series.  See the review for Graphics Gems by Andrew Glassner for more information.

(1994) cover Graphics Gems IV
edited by Paul Heckbert
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This book is part of the excellent Graphics Gems I-V series.  See the review for Graphics Gems by Andrew Glassner for more information.

(1994) cover Graphics Gems III
edited by David Kirk
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This book is part of the excellent Graphics Gems I-V series.  See the review for Graphics Gems by Andrew Glassner for more information.

(1994) Graphics Gems II
edited by James Arvo
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This book is part of the excellent Graphics Gems I-V series.  See the review for Graphics Gems by Andrew Glassner for more information.

(1994) Geometric Concepts for Geometric Design 
by Wolfgang Boehm & Hartmut Prautzsch
New: $59.00 
This book could be subtitled: The Mathematical Foundations of Computer Graphics.  It gives an excellent overview of many areas of math used in CG: linear algebra, perspective viewing, reconstruction, affine geometry, projective geometry, basic algebraic geometry and differential geometry.  However, it does not include many applications, and has no algorithms.  In short, it is a math book, but is restricted to math usually used in computer applications.  The presentation is very clear, to the point, and should be comprehensible to most graphics programmers.  It would be a useful reference (or text) giving thorough coverage of much of the math that underlies computational geometry.

(1992) cover Advanced Animation and Rendering Techniques
by Alan Watt & Mark Watt
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This is definitely an "advanced" text covering many computer graphics techniques.  It is divided into four parts: I Basics, II Theory, III Rendering, and IV Animation.  The single chapter (30 pages) Basics jumps right into 3D polygon modeling, hidden surface removal, plus Goraud and Phong shading algorithms.  Then onto the advanced stuff !  By Chapter 3 in Part II, the Watts have completed an in depth description of all the important spline curves and surfaces (Bezier, B-spline, beta, and NURBS).  The large Part III (Chapters 5-14) gives detailed treatments of shadows, texture, ray tracing (3 Chapters), radiosity, and illumination.  The final Part IV is an introduction to motion control, figure animation, and surface deformations.  If you're serious about computer graphics, this is a great book with a lot of detailed and well-explained material.  It is definitely not for beginners, but with a strong math background one could jump right in for an "advanced" crash course.  It is definitely readable with a good expository style.

(1990) Graphics Gems
edited by Andrew Glassner
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This outstanding series has algorithms of all types, with "C" code, for computer graphics and computational geometry.  Includes many fundamental geometry algorithms, especially for those special cases that always show up in practice.  Code from this series can be downloaded from the Graphics Gems Repository.  Each volume has sections for significant areas of graphics such as "Geometry", "Image Processing", "Ray Tracing", etc.  However, there is no clear structural attempt to give comprehensive coverage of a topic, and the format is more like a potpourri - all books and chapters are independent.  Nevertheless, taken together these books provide a large number of known practical algorithms.  The journal of graphics tools is a follow-on to this book series.

(1989) cover An Introduction to Ray Tracing
by Andrew Glassner (Editor)
New: $87.20  List: $109.00 
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An essential reference for this visualization technique.

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