MATHEMATICAL ELEMENTS FOR COMPUTER GRAPHICS Second Edition by David F. Rogers & J. Allen Adams

 TABLE of CONTENTS Foreword to the First Edition xi Preface xiii Preface to the First Edition xvii 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 Index 599 Order from Barnes & Noble Back to Books Page

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