# Computer Graphics and Geometric Modeling

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

### Popular passages

Page xviii - To me, style is just the outside of content, and content the inside of style, like the outside and inside of the human body — both go together, they can't be separated" (Richard Roud, Jean-Luc Godard, Indianapolis, IN: Indiana University Press, 1970).

### References to this book

 Geometric Tools for Computer GraphicsNo preview available - 2003
 Fundamentals of Computer GraphicsNo preview available - 2005
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