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This is a volume in,The Graphics Gems Series,A Collection of Practical Techniques. for the Computer Graphics Programmer,Series Editor. Andrew S Glassner,Xerox Palo Alto Research Center,Palo Alto Califomia. JAMES ARVO,Program of Computer Graphics,Cornell University. Ithaca New York,AP PROFESSIONAL,Boston San Diego NewYork.
London Sydney Tokyo Toronto,Copyright c 1995 by Academic Press Inc. GRAPHICS GEMS copyright c 1990 by Academic Press Inc. GRAPHICS GEMS II copyright c 1991 by Academic Press Inc. GRAPHICS GEMS III copyright c 1992 by Academic Press Inc. QUICK REFERENCE TO COMPUTER GRAPHICS TERMS,copyright c 1993 by Academic Press Inc. RADIOSITY AND REALISTIC IMAGE SYNTHESIS,copyright c 1993 by Academic Press Inc. VIRTUAL REALITY APPLICATIONS AND EXPLORATIONS,copyright c 1993 by Academic Press Inc. All rights reserved, No part of this product may be reproduced or transmitted in any form or by any.
means electronic or mechanical including input into or storage in any information. system other than for uses specified in the License Agreement without permission. in writing from the publisher, Except where credited to another source the C and C Code may be used freely to. modify or create programs that are for personal use or commercial distribution. Produced in the United States of America,ISBN 0 12 059756 X. About the Cover, The cover image is the second in the Gems theme that I began last year Andrew. Glassner and I bounced some ideas back and forth and the design solidified pretty. quickly The gems themselves are the same as in last year s image The picture was. generated at Pacific Data Images using their in house software All of the textures and. models are procedurally generated The sand texture the sand surface shape the. woodgrain the sea foam and the starfish texture are all derived from fractal noise. patterns I spent most of my time on the water making it look all shiny and wet and. transparent but not too transparent The foam on the water s surface was also very time. consuming Another challenge was to get the gems to all pile on top of each other. convincingly I wrote a program that dropped them one at a time and as they fell they. were rotated to the angle that moved them the furthest down without intersecting. anything that was there already This program took a couple of hours to run but it was. much faster than trying to place them by hand The picture was rendered with a ray. tracing program and took 50 hours on an Silicon Graphics 4D25 computer at a resolution. of 2250 3000 pixels with four samples per pixel,Thaddeus Beier. Silicon Graphics Computer Systems, When Andrew asked if I wanted to do the cover for Graphics Gems II I said Sure.
we can reuse the software we built last year for Graphics Gems While it wasn t quite. that simple it was much easier to produce this cover than the first one As before the. image was designed on a color monitor producing red green and blue pixels For. printing we needed to convert these pixels to cyan magenta yellow and black pixels. printer color space Once in this form the image was processed commercially to. produce half toned film suitable for printing This final step was performed at Kedie. Orent Sunnyvale California on their Crosfield digital prepress system. As was the case with the first Gems picture many of the original image colors could. not be exactly reproduced in print form The colors had to be modified to map into the. set of colors that can be produced by the printer its gamut The trick is to do the. modification while maintaining the appearance of the image In this picture the colors. in the sand shells and water were mostly inside the printer gamut However some of. the gem colors particularly the bright blue greens were far outside the gamut The. transformation we applied was similar to the one we designed for Graphics Gems colors. outside of the gamut were desaturated to colors of the same lightness while maintaining. the same hue If one color of a particular hue needed to be desaturated all colors of. the same hue would be desaturated to preserve shading detail However colors outside. of the gamut move more than colors inside of the gamut to maintain the overall. saturation, The colors of the Graphics Gems II cover are lighter and more delicate than the cover. of Graphics Gems and much more of the image lies in the interior of the printer gamut. We tuned the transformation for this image to minimize the change to the less saturated. colors preserving the subtle shading in the sand and water. Thanks to Bill Wallace who wrote the original gamut mapping software for Graphics. Gems and to Ken Fishkin who helped with the production of the cover this year. Maureen Stone,Xerox Palo Alto Research Center, The symbol C denotes gems that have accompanying C implementations on disk. By Andrew Glassner xvii,Preface xix,Mathematical Notation xxi. Pseudo Code xxiii,Contributors xxix,2 D GEOMETRY AND ALGORITHMS. Introduction 3,1 The Area of a Simple Polygon 5,2 Intersection of Line Segments C 7.
Mukesh Prasad,3 Distance from a Point to a Line 10. Jack C Morrison,4 An Easy Bounding Circle 14, 5 The Smallest Circle Containing the Intersection C. of Two Circles 17,6 Appolonius s 10th Problem 19,7 A Peano Curve Generation Algorithm C 25. Ken Musgrave, 8 Space Filling Curves and a Measure of Coherence C 26. Douglas Voorhies,9 Scanline Coherent Shape Algebra 31.
Jonathan E Steinhart,I MAGE PROCESSING,Introduction 49. 1 Image Smoothing and Sharpening by Discrete,Convolution 50. Dale A Schumacher, 2 A Comparison of Digital Halftoning Techniques C 75. Dale A Schumacher,3 Color Dithering C 72,Spencer W Thomas and Rod G Bogart. 4 Fast Anamorphic Image Scaling 78,Dale A Schumacher.
5 Real Pixels 80,6 A Fast 90 Degree Bitmap Rotator C 84. Sue Ken Yap,7 Rotation of Run Length Encoded Image Data C 86. 8 Adaptive Run Length Encoding 89,Andrew S Glassner. 9 Image File Compression Made Easy 93,Alan W Paeth. 10 An Optimal Filter for Image Reconstruction 101,Nelson Max.
11 Noise Thresholding in Edge Images 105,John Schlag. 12 Computing the Area the Circumference and the Genus. of a Binary Digital Image C 107,Hanspeter Bieri and Andreas Kohler. F RAME BUFFER TECH,RAME N IQUES,Introduction 115,1 Efficient Inverse Color Map Computation C 116. Spencer W Thomas, 2 Efficient Statistical Computations for Optimal Color. Quantization 126,Xiaolin Wu,3 A Random Color Map Animation Algorithm C 134.
Ken Musgrave,4 A Fast Approach to PHIGS PLUS Pseudo Color 138. James Hall and Terence Lindgren,5 Mapping RGB Triples onto 16 Distinct Values 143. 6 Television Color Encoding and Hot Broadcast,Colors C 147. David Martindale and Alan W Paeth,7 An Inexpensive Method of Setting the Monitor. White Point 159,Gary W Meyer,8 Some Tips for Making Color Hardcopy 163.
Ken Musgrave,3 D GEOMETRY AND ALGORITHMS,Introduction 169. 1 Area of Planar Polygons and Volume of Polyhedra 170. Ronald N Goldman,2 Getting Around on a Sphere 172,Clifford A Shaffer. 3 Exact Dihedral Metrics for Common Polyhedra 174,Alan W Paeth. 4 A Simple Viewing Geometry 179,Andrew S Glassner,5 View Correlation C 181. Rod G Bogart,6 Maintaining Winged Edge Models 191,Andrew S Glassner.
7 Quadtree Octree to Boundary Conversion 202,Claudio Montani and Roberto Scopigno. 8 Three Dimensional Homogeneous Clipping,of Triangle Strips C 219. Patrick Gilles Maillot,9 InterPhong Shading C 232,Nadia Magnenat Thalmann Daniel Thalmann. and Hong Tong Minh,R AY TRACING,Introduction 245,1 Fast Ray Convex Polyhedron Intersection C 247. Eric Haines, 2 Intersecting a Ray with an Elliptical Torus C 251.
Joseph M Cychosz, 3 Ray Triangle Intersection Using Binary Recursive. Subdivision 257,Douglas Voorhies and David Kirk, 4 Improved Ray Tagging for Voxel Based Ray Tracing 264. David Kirk and James Arvo,5 Efficiency Improvements for Hierarchy Traversal. in Ray Tracing 267,Eric Haines,6 A Recursive Shadow Voxel Cache for Ray. Tracing C 273,Andrew Pearce,7 Avoiding Incorrect Shadow Intersections for Ray.
Tracing 275,Andrew Pearce,8 A Body Color Model Absorption of Light through. Translucent Media 277,Mark E Lee and Samuel P Uselton. 9 More Shadow Attenuation for Ray Tracing Transparent. or Translucent Objects 283,Mark E Lee and Samuel P Uselton. R ADIOSITY,Introduction 293,1 Implementing Progressive Radiosity with User. Provided Polygon Display Routines C 295,Shenchang Eric Chen.
2 A Cubic Tetrahedral Adaptation of the Hemi Cube,Algorithm 299. Jeffrey C Beran Koehn and Mark J Pavicic,3 Fast Vertex Radiosity Update C 303. Filippo Tampieri,4 Radiosity via Ray Tracing 306,Peter Shirley. 5 Detection of Shadow Boundaries for Adaptive Meshing. in Radiosity 311,Fran ois Sillion,M ATRIX TECHNIQUES. Introduction 319,1 Decomposing a Matrix into Simple.
Transformations C 320,Spencer W Thomas, 2 Recovering the Data from the Transformation Matrix 324. Ronald N Goldman,3 Transformations as Exponentials 332. Ronald N Goldman,4 More Matrices and Transformations Shear and. Pseudo Perspective 338,Ronald N Goldman,5 Fast Matrix Inversion C 342. 6 Quaternions and 4 4 Matrices 351,Ken Shoemake,7 Random Rotation Matrices C 355.
James Arvo,8 Classifying Small Sparse Matrices C 357. James Arvo,N UMERICAL AND PROGRAMMING,T ECHNIQUES,Introduction 365. 1 Bit Picking 366,Ken Shoemake,2 Faster Fourier Transform 368. Ken Shoemake,3 Of Integers Fields and Bit Counting C 371. Alan W Paeth and David Schilling,4 Using Geometric Constructions to Interpolate.
Orientation with Quaternions 377,John Schlag, 5 A Half Angle Identity for Digital Computation 381. The Joys of the Halved Tangent,Alan W Paeth,6 An Integer Square Root Algorithm C 387. Christopher J Musial,7 Fast Approximation to the Arctangent 389. Ron Capelli,8 Fast Sign of Cross Product Calculation C 392. Jack Ritter,9 Interval Sampling 394,Ken Shoemake, 10 A Recursive Implementation of the Perlin Noise Function C 396.
C URVES AN,ANDD SURFACES,Introduction 405,1 Least Squares Approximations to B zier Curves. and Surfaces 406,Doug Moore and Joe Warren,2 Beyond B zier Curves 412. Ken Shoemake,3 A Simple Formulation for Curve Interpolation. with Variable Control Point Approximation 417,John Schlag. 4 Symmetric Evaluation of Polynomials 420,Terence Lindgren.
5 Menelaus s Theorem 424,Hans Peter Seidel, 6 Geometrically Continuous Cubic B zier Curves 428. Hans Peter Siedel, 7 A Good Straight Line Approximation of a Circular. Christopher J Musial,8 Great Circle Plotting 440,Alan W Paeth. 9 Fast Anti Aliased Circle Generation 446,Xiaolin Wu.

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