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This text is ideal for junior-, senior-, and graduate-level courses in computer graphics and computer-aided design taught in departments of mechanical and aeronautical engineering and computer science. It presents in a unified manner an introduction to the mathematical theory underlying computer graphic applications. It covers topics of keen interest to students in engineering and computer science: transformations, projections, 2-D and 3-D curve definition schemes, and surface definitions. It also includes techniques, such as B-splines, which are incorporated as part of the software in advanced engineering workstations. A basic knowledge of vector and matrix algebra and calculus is required.

- Sales Rank: #1487262 in Books
- Published on: 1989-08-01
- Original language: English
- Number of items: 1
- Dimensions: 9.20″ h x 1.40″ w x 6.30″ l,
- Binding: Paperback
- 512 pages

Most helpful customer reviews

3 of 3 people found the following review helpful.

One of the best books I’ve read.

By Joseph R. Kennedy

This was one of the coolest technology books I’ve read, since I loved the topic and it was well written and explained. Please buy it if you want to know the theory behind computer graphics (like how the videocard and monitor interact to draw pixils on the screen and polygons as well) otherwise save your money if you think this will help you MAKE computer graphics. This book is all interesting theory and nothing to do with actually making the graphics themselves, unless you plan on doing it with a 1970’s computer or writing your own graphics card bios or driver (or maybe a rewrite of directx?)

10 of 10 people found the following review helpful.

Clear presentation of the mathematics behind computer graphics

By calvinnme

This old book is a very good programming language-independent guide to the mathematics necessary for the implementation of computer graphics. I still consult my copy regularly even now, 14 years after I first purchased it. Chapter one, on computer graphics basics in general, talks about very old hardware technology, and can largely be skipped. Who really needs to know about dot matrix printers and electrostatic plotters these days? Chapter 2 begins the meat of the book, where the 2D matrix transformations of scaling, translation, rotation, and reflection are introduced. Next the author shows how to combine these matrices to perform these operations in series. These ideas are extended to 3D in chapter 3. The latter part of chapter 3 might be of particular interest to students of computer vision, since it does an exceptional job of explaining the mathematics of perspective, vanishing points, projection, and reconstruction of 3D images that so many computer vision books tend to gloss over. Chapters 4 through 6 is where the book is truly excellent, in that it gives the clearest presentation of parametric curves, B-splines, and Bezier curves I have ever seen, and then extends these ideas to full-fledged 3D objects and surfaces. Plenty of diagrams and equations are shown throughout the book, but code implementations are left to the reader. If you are interested in more modern techniques such as quaternions, there is none of that here due to the age of the book. This same author has an entirely separate book that is also excellent, “Procedural Elements of Computer Graphics”, for the less mathematical algorithmic portions of computer graphics. Amazon does not show the table of contents, so I do that here for the purpose of completeness:

Chapter 1 Introduction To Computer Graphics 1

1-1 Overview of Computer Graphics 3

1-2 Representing Pictures 3

1-3 Preparing Pictures For Presentation 5

1-4 Presenting Previously Prepared Pictures 6

1-5 Interacting with the Picture 9

1-6 Description of Some Graphics Devices 18

1-7 Storage Tube Graphics Displays 18

1-8 Calligraphic Refresh Graphics Displays 19

1-9 Raster Refresh Graphics Displays 24

1-10 Cathode Ray Tube Basics 30

1-11 Color CRT Raster Scan Basics 31

1-12 Video Basics 32

1-13 Flat Panel Displays 35

1-14 Electrostatic Plotters 42

1-15 Laser Printers 44

1-16 Dot Matrix Plotters 47

1-17 Ink Jet Plotters 49

1-18 Thermal Plotters 50

1-19 Pen and Ink Plotters 52

1-20 Color Film Cameras 56

1-21 Active and Passive Graphics Devices 57

1-22 Computer Graphics Software 58

1-23 References 59

Chapter 2 Two-Dimensional Transformations 61

2-1 Introduction 61

2-2 Representation of Points 61

2-3 Transformations and Matrices 62

2-4 Transformation of Points 62

2-5 Transformation of Straight Lines 65

2-6 Midpoint Transformation 66

2-7 Transformation of Parallel Lines 68

2-8 Transformation of Intersecting Lines 69

2-9 Rotation 72

2-10 Reflection 76

2-11 Scaling 78

2-12 Combined Transformations 80

2-13 Transformation of The Unit Square 83

2-14 Solid Body Transformations 86

2-15 Translations and Homogeneous Coordinates 87

2-16 Rotation About an Arbitrary Point 88

2-17 Reflection Through an Arbitrary Line 89

2-18 Projection – A Geometric Interpretation of Homogeneous Coordinates 90

2-19 Overall Scaling 94

2-20 Points At Infinity 95

2-21 Transformation Conventions 98

2-22 References 100

Chapter 3 Three-Dimensional Transformations 101

3-1 Introduction 101

3-2 Three-Dimensional Scaling 102

3-3 Three-Dimensional Shearing 106

3-4 Three-Dimensional Rotation 107

3-5 Three-Dimensional Reflection 113

3-6 Three-Dimensional Translation 115

3-7 Multiple Transformations 115

3-8 Rotations About an Axis Parallel to a Coordinate Axis 117

3-9 Rotation About an Arbitrary Axis in Space 121

3-10 Reflection Through an Arbitrary Plane 128

3-11 Affine and Perspective Geometry 132

3-12 Orthographic Projections 135

3-13 Axonometric Projections 141

3-14 Oblique Projections 151

3-15 Perspective Transformations 157

3-16 Techniques For Generating Perspective Views 171

3-17 Vanishing Points 179

3-18 Photography and The Perspective Transformation 185

3-19 Stereographic Projection 187

3-20 Comparison of Object Fixed and Center of Projection Fixed Projections 195

3-21 Reconstruction of Three-Dimensional Images 200

3-22 References 206

Chapter 4 Plane Curves 207

4-1 Introduction 207

4-2 Curve Representation 207

4-3 Nonparametric Curves 209

4-4 Parametric Curves 211

4-5 Parametric Representation of a Circle 215

4-6 Parametric Representation of an Ellipse 218

4-7 Parametric Representation of a Parabola 223

4-8 Parametric Representation of a Hyperbola 227

4-9 A Procedure For Using Conic Sections 231

4-10 The General Conic Equations 231

4-11 References 246

Chapter 5 Space Curves 247

5-1 Introduction 247

5-2 Representation of Space Curves 248

5-3 Cubic Splines 250

5-4 Normalized Cubic Splines 267

5-5 Alternate Cubic Spline End Conditions 271

5-6 Parabolic Blending 278

5-7 Generalized Parabolic Blending 284

5-8 Bezier Curves 289

5-9 B-spline Curves 305

5-10 End Conditions For Periodic B-spline Curves 339

5-11 B-spline Curve Fit 346

5-12 B-spline Curve Subdivision 351

5-13 Rational B-spline Curves 356

5-14 References 375

Chapter 6 Surface Description and Generation 379

6-1 Introduction 379

6-2 Surfaces of Revolution 380

6-3 Sweep Surfaces 394

6-4 Quadric Surfaces 400

6-5 Piecewise Surface Representation 408

6-6 Mapping Parametric Surfaces 411

6-7 Bilinear Surface 414

6-8 Ruled and Developable Surfaces 417

6-9 Linear Coons Surface 422

6-10 Coons Bicubic Surface 426

6-11 Bezier Surfaces 435

6-12 B-spline Surfaces 445

6-13 B-spline Surface Fitting 456

6-14 B-spline Surface Subdivision 458

6-15 Gaussian Curvature and Surface Fairness 461

6-16 Rational B-spline Surfaces 465

6-17 References 477

Appendices 481

Appendix A Computer Graphics Software 481

Appendix B Matrix Methods 503

Appendix C Pseudocode 507

Appendix D B-Spline Surface File Format 513

Appendix E Problems 517

Appendix F Programming Projects 527

Appendix G Algorithms 541

3 of 6 people found the following review helpful.

Mathematical Elements for Computer Graphics

By A Customer

While written over 24 years ago, I was hoping this book would give me an understanding of the mathematical basis (if not the current state-of-the art;) ) of computer graphics. Despite (arguable to many) years of university math courses, I found this volume merely humbling, rather than enlightening. If you are more comfortable with fairly advanced mathematical notation and concepts than most, especially relative to geometry, you may find this book useful. I found it only marginally useful — primarilly as a reference to some concepts I had previously been exposed. Best of luck.

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