Computer Graphics and Geometric Modeling

Front Cover
Springer Science & Business Media, 1999 - Computers - 851 pages
This is a book for those interested in understanding how graphics programs work and how present-day computer graphics can generate reallistic-looking curves, surfaces, and solid objects. The book emphasizes the mathematics behind computer graphics and most of the required math is included in an appendix. The main topics covered are: -scan conversion methods; selecting the best pixels for generating lines, circles and other objects -geometric transformations and projections; translations, rotations, moving in 3d, perspective projections -curves and surfaces; construction, wire-frames, rendering, normals -other topics; CRTs, antialiasing, animation, color, perception, polygons, compression. With its numerous illustrative examples and exercises, the book makes a splendid text for a two-semester course in computer graphics for advanced undergraduates or graduate students. It also serves a fine reference for professionals in the computer graphics field.
 

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Contents

First Principles
xix
2 Bitmap Scaling
14
3 Bitmap Rotation
18
4 A Practical Drawing Program
21
ScanConverting Methods
25
2 Midpoint Subdivision
26
4 DoubleStep DDA
32
5 BestFit DDA
36
18 Surfaces of Revolution
514
19 Sweep Surfaces
524
20 Polygonal Surfaces by Subdivision
528
21 Curves on Surfaces
531
22 Surface Normals
533
Rendering
535
2 A Simple Shading Model
536
3 Gouraud and Phong Shading
546

6 ScanConverting in Parallel
37
7 ScanConverting Circles
40
8 Thick Curves
47
9 Antialiasing
48
Transformations and Projections
57
2 TwoDimensional Transformations
59
3 Windowing
86
4 Clipping
88
5 ThreeDimensional Transformations
89
6 Transforming the Coordinate System
100
7 Projections
101
9 Perspective Projections
110
Stereo Image
135
11 The Viewing Volume
139
12 Going Beyond the Third Dimension
142
13 Nonlinear Projections
151
2 Parametric Blending
178
3 Curve Representations
179
4 The Lagrange Polynomial
196
5 The Newton Polynomial
203
6 Spline Methods for Curves
204
7 Hermite Interpolation
205
8 The Cubic Spline Curve
223
9 The Quadratic Spline
245
10 Cardinal Splines
246
CatmullRom Curves
249
12 KochanekBartels Splines
256
13 Fitting a PC to Experimental Points
260
14 The B6zier Curve
264
15 Subdivision Curves
319
16 The BSpline
326
17 The Beta Spline
387
18 Barycentric Sums Revisited
391
19 Symmetry in Curves
392
20 Conic Sections
395
21 Parametric Space of a Curve
399
22 Curvature and Torsion
400
23 The Hough Transform
408
Surfaces
413
2 Basic Concepts
415
3 Polygonal Surfaces
417
4 Delaunay Triangulation
425
5 Bilinear Surfaces
432
6 Lofted Surfaces
437
7 Coons Surfaces
441
8 The Cartesian Product
454
9 The Biquadratic Surface Patch
455
10 The Bicubic Surface Patch
457
11 CatmullRom Surfaces
466
12 Rectangular Bezier Surfaces
469
13 Triangular Braior Surfaces
481
14 Converting Bezier Patches
486
15 The Gregory Patch
493
16 Gordon Surfaces
496
17 Uniform BSpline Surfaces
497
4 Palette Optimization
547
5 Ray Tracing
549
6 Texturing
550
7 Bump Mapping
552
Color
555
2 The HLS Color Model
557
4 The RGB Color Model
559
5 Additive and Subtractive Colors
561
6 Complementary Colors
565
Computer Animation
573
2 Interpolating Positions
576
I
581
II
591
5 Nonuniform Interpolation
598
6 Morphing
604
7 FreeForm Deformations
605
Image Compression
607
1 Introduction
608
2 VariableSize Codes
609
3 RunLength Encoding
610
4 Fax Compression
613
5 Cell Encoding
620
6 Quadtrees
622
7 Progressive Image Compression
628
8 FELICS
632
9 The Golomb Code
640
10 Progressive FELICS
641
11 MLP
644
12 Differential Lossless Image Compression
652
13 Wavelets
654
Short Topics
659
2 Boundary Fill
666
3 Halftoning
667
4 Dithering
669
5 Fractals
678
6 A Fractal Line
679
7 Branching Rules
682
8 Iterated Function Systems IFS
683
9 Image Processing
686
Mathematical Topics
691
2 Forward Differences
696
3 Coordinate Systems
698
4 Vector Algebra
700
5 Matrices
707
6 Trigonometric Identities Basic Identities
709
7 The Greek Alphabet
713
8 Complex Numbers
714
9 Quaternions
715
10 Groups
717
11 Fields
718
References
721
Answers to Exercises
731
Index
831
Copyright

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