Graphics Gems I / Edition 1

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"The GRAPHICS GEMS Series" was started in 1990 by Andrew Glassner. The vision and purpose of the Series was - and still is - to provide tips, techniques, and algorithms for graphics programmers. All of the gems are written by programmers who work in the field and are motivated by a common desire to share interesting ideas and tools with their colleagues. Each volume provides a new set of innovative solutions to a variety of programming problems.

Computer Graphics compiles the "tricks of the trade" in computer graphics--collected from over 50 different programmers around the world. Between these covers are more than 100 different ideas, methods, and techniques that anyone can use in graphics programming, ranging from basic geometry to specific algorithms.

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Editorial Reviews

Contains more than one hundred ideas, methods and techniques to use in graphics programming. They range from basic geometry to specific algorithms in fields like anti-aliased line drawing, texture mapping, splines and polygon rendering. Many of these techniques contain public domain implementations, complete and ready-to-run, in the C language. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780122861666
  • Publisher: Elsevier Science
  • Publication date: 6/29/1993
  • Series: Graphics Gems - IBM Series
  • Edition description: Reissue
  • Edition number: 1
  • Pages: 864
  • Product dimensions: 7.71 (w) x 9.56 (h) x 1.72 (d)

Meet the Author

Andrew Glassner's contributions to computer graphics span 20 years. His work at Microsoft Research, Xerox PARC, the IBM Watson Research Labs, Bell Communications Research, and the Delft University of Technology has produced numerous technical articles on rendering theory and practice, animation, modeling, and new media. He currently creates new computer graphics tools at Microsoft Research. Among his recent work is Chicken Crossing, a 3D animated short film that has been shown internationally at film festivals and on television, and Dead Air, an interactive game for play over the Internet. Dr. Glassner is the author of the two volume bible, Principles of Digital Image Synthesis and 3D Computer Graphics: A Handbook for Artists and Designers. He has also edited An Introduction to Ray Tracing, and created the Graphics Gems series for programmers.

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Table of Contents

Italic page numbers refer to location of corresponding C implementation.
Preface ..... xv
Introduction ..... xvii
Mathematical Notation ..... xix
Pseudo-Code ..... xxi
Contributors ..... xxvi

1 -- 2D Geometry
Useful 2D Geometry ..... 3
Trigonometry Summary ..... 12
Useful Trigonometry ..... 13
Trigonometric Functions at Select Points ..... 18
Triangles ..... 20
Generating Random Points In Triangle (649) ..... 24
Fast Line-Edge Intersections on a Uniform Grid (651) ..... 29
Anti-Aliasing Summary ..... 37
Area of Intersection: Circle and a Half-Plane ..... 38
Area of intersection: Circle and a Thick Line ..... 40
Area of Intersection: Two Circles ..... 43
Vertical Distance from a Point to a Line ..... 47
A Fast 2D Point-on-Line Test (654) ..... 49
Fast Circle-Rectangle Intersection Checking (656) ..... 51

2 -- 2D Rendering
Circles of Integral Radius on Integer Lattices ..... 57
Nice Numbers for Graph Labels (657) ..... 61
Efficient Generation of Sampling Jitter Using Look-up Tables (660) ..... 64
Scan Conversion Summary ..... 75
Fast Anti-Aliasing Polygon Scan Conversion (662) ..... 76
Generic Convex Polygon Scan Conversion and Clipping (667) ..... 84
Concave Polygon Scan Conversion (681) ..... 87
Fast Scan Conversion of Arbitrary Polygons ..... 92
Line-Drawing Summary ..... 98
Digital Line Drawing (685) ..... 99
Symmetric Double Step Line Algorithm (686) ..... 101
Rendering Anti-Aliased Lines (690) ..... 105
An Algorithm for Filling in 2D Wide Line Bevel Joints ..... 107
Rendering Fat Lines on a Raster Grid ..... 114
Two-Dimensional Clipping: A Vector-Based Approach (694) ..... 121
Periodic Tilings of the Plane on a Raster Grid ..... 129

3 -- Image Processing
Anti-Aliasing Filters Summary ..... 143
Convenient Anti-Aliasing Filters That Minimize &Bumpy& Sampling ..... 144
Filters for Common Resampling Tasks ..... 147
Smoothing Enlarged Monochrome Images ..... 166
Median Finding on a 3 x 3 Grid (711) ..... 171
Ordered Dithering (713) ..... 176
A Fast Algorithm for General Raster Rotation ..... 179
Useful 1-to-1 Pixel Transforms ..... 196
Alpha Blending ..... 210

4 -- Frame Buffer Techniques
Frame Buffers and Color Maps ..... 215
Reading a Write-Only Write Mask ..... 219
A Digital "Dissolve" Effect (715) ..... 221
Mapping RGB Triples onto Four Bits (718) ..... 233
What Are the Coordinates of a Pixel? ..... 246
Proper Treatment of Pixels as Integers (719) ..... 249
Normal Coding ..... 257
Recording Animation in Binary Order for Progressive Temporal Refinement (720) ..... 265
1-to-1 Pixel Transforms Optimized through Color-Map Manipulation ..... 270
A Seed Fill Algorithm (721) ..... 275
Filling a Region in a Frame Buffer ..... 278
Precalculating Addresses for Fast Fills, Circles, and Lines ..... 285
A Simple Method for Color Quantization: Octree Quantization ..... 287

5 -- 3D Geometry
Useful 3D Geometry ..... 297
An Efficient Bounding Sphere (723) ..... 301
Intersection of Two Lines in Three-Space ..... 304
Intersection of Three Planes ..... 305
Mapping Summary ..... 306
Digital Cartography for Computer Graphics ..... 307
Albers Equal-Area Conic Map Projection (726) ..... 321
Boxes and Sphere Summary ..... 326
Spheres-to-Voxels Conversion ..... 327
A Simple Method for Box-Sphere Intersection Testing (730) ..... 335

6 -- 3D Rendering
3D Grid Hashing Function (733) ..... 343
Backface Culling ..... 346
Fast Dot Products for Shading ..... 348
Scanline Depth Gradient of a Z-Buffered Triangle ..... 361
Simulating Fox and Haze ..... 3 64
Interpretation of Texture Map Indices ..... 366
Multidimensional Sum Tables ..... 376

7 -- Ray Tracing

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