Computer Graphics and Geometric Modeling

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Springer Science & Business Media, Dec 6, 2012 - Computers - 852 pages
Joseph-Louis Lagrange (1736-1813), one of the greatest mathematicians of the 18th century, made important contributions to the theory of numbers and to analytical and celestial mechanics. His most important work is Mecanique Analytique (1788), the textbook on which all subsequent work in this field is based. A contempo rary reader is surprised to find no diagrams or figures of any kind in this book on mechanics. This reflects one extreme approach to graphics, namely considering it unimportant or even detracting as a teaching tool and not using it. Today, of course, this approach is unthinkable. Graphics, especially computer graphics, is commonly used in texts, advertisements, and movies to illustrate concepts, to emphasize points being discussed, and to entertain. Our approach to graphics has been completely reversed since the days of La grange, and it seems that much of this change is due to the use of computers. Computer graphics today is a mature, successful, and growing field. It is used by many people for many purposes and it is enjoyed by even more people. One criterion for the maturity of a field of study is its size. When a certain discipline becomes so big that no one person can keep all of it in their head, we say that that discipline has matured (or has come of age). This is what happened to computer graphics in the last decade or so.
 

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Contents

First Principles
1
ScanConverting Methods
27
Transformations and Projections
58
Curves
173
Points and Vectors
174
Parametric Blending
180
Curve Representations
181
The Lagrange Polynomial
198
Texturing
552
Bump Mapping
554
Color 1 Color and the Eye
557
The HLS Color Model
559
The RGB Color Model
561
Additive and Subtractive Colors
563
Complementary Colors
567
The CIE Standard
571

The Newton Polynomial
205
Spline Methods for Curves
206
Hermite Interpolation
207
The Cubic Spline Curve
225
The Quadratic Spline
247
Cardinal Splines
248
CatmullRom Curves
251
KochanekBartels Splines
258
Fitting a PC to Experimental Points
262
The Bézier Curve
266
Subdivision Curves
321
The BSpline
328
The Beta Spline
389
Barycentric Sums Revisited
393
Symmetry in Curves
394
Conic Sections
397
Parametric Space of a Curve
401
Curvature and Torsion
402
The Hough Transform
410
Surfaces 415
414
Input ThreeDimensional Points
416
Basic Concepts
417
Polygonal Surfaces
419
Delaunay Triangulation
427
Bilinear Surfaces
434
Lofted Surfaces
439
Coons Surfaces
443
The Cartesian Product
456
The Biquadratic Surface Patch
457
The Bicubic Surface Patch
459
CatmullRom Surfaces
468
Rectangular Bézier Surfaces
471
Triangular Bézier Surfaces
483
Converting Bézier Patches
488
The Gregory Patch
495
Gordon Surfaces
498
Uniform BSpline Surfaces
499
Surfaces of Revolution
516
Sweep Surfaces
526
Polygonal Surfaces by Subdivision
530
Curves on Surfaces
533
Surface Normals
535
Rendering 1 Introduction
537
A Simple Shading Model
538
Gouraud and Phong Shading
548
Palette Optimization
549
Ray Tracing
551
Computer Animation 1 Background
575
Interpolating Positions
578
I
583
II
593
Nonuniform Interpolation
600
Morphing
606
FreeForm Deformations
607
Image Compression
609
Introduction
610
VariableSize Codes
611
RunLength Encoding
612
Fax Compression
615
Cell Encoding
622
Quadtrees
624
Progressive Image Compression
630
FELICS
634
The Golomb Code
642
Progressive FELICS
643
MLP
646
Differential Lossless Image Compression
654
Wavelets
656
Graphics Standards
661
Boundary Fill
668
Halftoning
669
Dithering
671
Fractals
680
A Fractal Line
681
Branching Rules
684
Iterated Function Systems IFS
685
Image Processing
688
Mathematical Topics 693
692
Forward Differences
698
Coordinate Systems
700
Vector Algebra
702
Matrices
709
Trigonometric Identities
711
The Greek Alphabet
715
Complex Numbers
716
Quaternions
717
Groups
719
Fields
720
References
723
Answers to Exercises 733
732
Index
833
609
842
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