Mathematical Structures for Computer Graphics (eBook)

STEVEN J. JANKE, PhD, is Professor of Mathematics and Computer Science at Colorado College. He has over 20 years of teaching experience in the field of computer graphics and is the coauthor of Introduction to Linear Models and Statistical Inference, also published by Wiley.

Preface iii

1 Basics 1

1.1 Graphics Pipeline 2

1.2 Mathematical Descriptions 5

1.3 Position 6

1.4 Distance 9

1.5 Complements and Details 13

1.6 Exercises 17

2 Vector Algebra 21

2.1 Basic Vector Characteristics 22

2.2 Two Important Products 31

2.3 Complements and Details 42

2.4 Exercises 46

3 Vector Geometry 49

3.1 Lines & Planes 49

3.2 Distances 55

3.3 Angles 63

3.4 Intersections 65

3.5 Additional Key Applications 73

3.6 Homogeneous Coordinates 86

3.7 Complements and Details 90

3.8 Exercises 94

4 Transformations 99

4.1 Types of Transformations 100

4.2 Linear Transformations 101

4.3 Three dimensions 113

4.4 Affine Transformations 123

4.5 Complements and Details 134

4.6 Exercises 145

5 Orientation 149

5.1 Cartesian Coordinate Systems 151

5.2 Cameras 159

5.3 Other Coordinate Systems 182

5.4 Complements and Details 190

5.5 Exercises 193

6 Polygons & Polyhedra 197

6.1 Triangles 197

6.2 Polygons 213

6.3 Polyhedra 230

6.4 Complements and Details 245

6.5 Exercises 250

7 Curves & Surfaces 255

7.1 Curve Descriptions 256

7.2 Bézier Curves 268

7.3 B-Splines 278

7.4 NURBS 295

7.5 Surfaces 300

7.6 Complements and Details 311

7.7 Exercises 316

8 Visibility 321

8.1 Viewing 321

8.2 Perspective Transformation 323

8.3 Hidden Surfaces 333

8.4 Ray Tracing 344

8.5 Complements and Details 351

8.6 Exercises 356

9 Lighting 359

9.1 Color Coordinates 359

9.2 Elementary Lighting Models 364

9.3 Global Illumination 384

9.4 Textures 391

9.5 Complements and Details 403

9.6 Exercises 408

10 Other Paradigms 411

10.1 Pixels 412

10.2 Noise 421

10.3 L-Systems 435

10.4 Exercises 443

A Geometry & Trigonometry 447

A.1 Triangles 447

A.2 Angles 449

A.3 Trigonometric Functions 450

B Linear Algebra 455

B.1 Systems of Linear Equations 455

B.2 Matrix Properties 458

B.3 Vector Spaces 460

"The book is suitable for undergraduate students of computer science, mathematics, and engineering, as well as an ideal reference for researchers and professionals in computer graphics." (Zentralblatt MATH, 1 June 2015)