Cover   MATHEMATICAL ELEMENTS

FOR

COMPUTER GRAPHICS

Second Edition

by

David F. Rogers & J. Allen Adams

 
 TABLE of CONTENTS
 
Foreword to the First Editionxi
Prefacexiii
Preface to the First Editionxvii
 
Chapter 1  Introduction To Computer Graphics1
1-1Overview of Computer Graphics3
1-2Representing Pictures3
1-3Preparing Pictures For Presentation5
1-4Presenting Previously Prepared Pictures6
1-5Interacting with the Picture9
1-6Description of Some Graphics Devices18
1-7Storage Tube Graphics Displays18
1-8Calligraphic Refresh Graphics Displays19
1-9Raster Refresh Graphics Displays24
1-10Cathode Ray Tube Basics30
1-11Color CRT Raster Scan Basics31
1-12Video Basics32
1-13Flat Panel Displays35
1-14Electrostatic Plotters42
1-15Laser Printers44
1-16Dot Matrix Plotters47
1-17Ink Jet Plotters49
1-18Thermal Plotters50
1-19Pen and Ink Plotters52
1-20Color Film Cameras56
1-21Active and Passive Graphics Devices57
1-22Computer Graphics Software58
1-23References59
 
Chapter 2  Two-Dimensional Transformations61
2-1Introduction61
2-2Representation of Points61
2-3Transformations and Matrices62
2-4Transformation of Points62
2-5Transformation of Straight Lines65
2-6Midpoint Transformation66
2-7Transformation of Parallel Lines68
2-8Transformation of Intersecting Lines69
2-9Rotation72
2-10Reflection76
2-11Scaling78
2-12Combined Transformations80
2-13Transformation of The Unit Square83
2-14Solid Body Transformations86
2-15Translations and Homogeneous Coordinates87
2-16Rotation About an Arbitrary Point88
2-17Reflection Through an Arbitrary Line89
2-18Projection - A Geometric Interpretation of 
 Homogeneous Coordinates90
2-19Overall Scaling94
2-20Points At Infinity95
2-21Transformation Conventions98
2-22References100
 
Chapter 3  Three-Dimensional Transformations101
3-1Introduction101
3-2Three-Dimensional Scaling102
3-3Three-Dimensional Shearing106
3-4Three-Dimensional Rotation107
3-5Three-Dimensional Reflection113
3-6Three-Dimensional Translation115
3-7Multiple Transformations115
3-8Rotations About an Axis Parallel to a 
 Coordinate Axis117
3-9Rotation About an Arbitrary Axis in Space121
3-10Reflection Through an Arbitrary Plane128
3-11Affine and Perspective Geometry132
3-12Orthographic Projections135
3-13Axonometric Projections141
3-14Oblique Projections151
3-15Perspective Transformations157
3-16Techniques For Generating Perspective Views171
3-17Vanishing Points179
3-18Photography and The Perspective Transformation185
3-19Stereographic Projection187
3-20Comparison of Object Fixed and Center of 
 Projection Fixed Projections195
3-21Reconstruction of Three-Dimensional Images200
3-22References206
 
Chapter 4  Plane Curves207
4-1Introduction207
4-2Curve Representation207
4-3Nonparametric Curves209
4-4Parametric Curves211
4-5Parametric Representation of a Circle215
4-6Parametric Representation of an Ellipse218
4-7Parametric Representation of a Parabola223
4-8Parametric Representation of a Hyperbola227
4-9A Procedure For Using Conic Sections231
4-10The General Conic Equations231
4-11References246
 
Chapter 5  Space Curves247
5-1Introduction247
5-2Representation of Space Curves248
5-3Cubic Splines250
5-4Normalized Cubic Splines267
5-5Alternate Cubic Spline End Conditions271
5-6Parabolic Blending278
5-7Generalized Parabolic Blending284
5-8Bezier Curves289
5-9B-spline Curves305
5-10End Conditions For Periodic B-spline Curves339
5-11B-spline Curve Fit346
5-12B-spline Curve Subdivision351
5-13Rational B-spline Curves356
5-14References375
 
Chapter 6  Surface Description and Generation379
6-1Introduction379
6-2Surfaces of Revolution380
6-3Sweep Surfaces394
6-4Quadric Surfaces400
6-5Piecewise Surface Representation408
6-6Mapping Parametric Surfaces411
6-7Bilinear Surface414
6-8Ruled and Developable Surfaces417
6-9Linear Coons Surface422
6-10Coons Bicubic Surface426
6-11Bezier Surfaces435
6-12B-spline Surfaces445
6-13B-spline Surface Fitting456
6-14B-spline Surface Subdivision458
6-15Gaussian Curvature and Surface Fairness461
6-16Rational B-spline Surfaces465
6-17References477
 
 Appendices481
 Appendix A   Computer Graphics Software481
 Appendix B   Matrix Methods503
 Appendix C   Pseudocode507
 Appendix D   B-Spline Surface File Format513
 Appendix E   Problems517
 Appendix F   Programming Projects527
 Appendix G   Algorithms541
 
 Index599
 
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