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
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