Mathematical Structures for Computer Graphics

Mathematical Structures for Computer Graphics

by Steven J. Janke
Released November 2014
Publisher(s): Wiley
ISBN: 9781118712191

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Book description

A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes

Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes.

Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant graphics details often overlooked in the literature. Rather than use a rigid theorem/proof approach, the book provides a flexible discussion that moves from vector geometry through transformations, curve modeling, visibility, and lighting models. Mathematical Structures for Computer Graphics also includes:

  • Numerous examples of two- and three-dimensional techniques along with numerical calculations
  • Plenty of mathematical and programming exercises in each chapter, which are designed particularly for graphics tasks
  • Additional details at the end of each chapter covering historical notes, further calculations, and connected concepts for readers who wish to delve deeper
  • Unique coverage of topics such as calculations with homogeneous coordinates, computational geometry for polygons, use of barycentric coordinates, various descriptions for curves, and L-system techniques for recursive images

Mathematical Structures for Computer Graphics is an excellent textbook for undergraduate courses in computer science, mathematics, and engineering, as well as an ideal reference for practicing engineers, researchers, and professionals in computer graphics fields. The book is also useful for those readers who wish to understand algorithms for producing their own interesting computer images.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. Chapter 1: Basics
    1. 1.1 Graphics Pipeline
    2. 1.2 Mathematical Descriptions
    3. 1.3 Position
    4. 1.4 Distance
    5. 1.5 Complements and Details
    6. 1.6 Exercises
  7. Chapter 2: Vector Algebra
    1. 2.1 Basic Vector Characteristics
    2. 2.2 Two Important Products
    3. 2.3 Complements and Details
    4. 2.4 Exercises
  8. Chapter 3: Vector Geometry
    1. 3.1 Lines and Planes
    2. 3.2 Distances
    3. 3.3 Angles
    4. 3.4 Intersections
    5. 3.5 Additional Key Applications
    6. 3.6 Homogeneous Coordinates
    7. 3.7 Complements and Details
    8. 3.8 Exercises
  9. Chapter 4: Transformations
    1. 4.1 Types of Transformations
    2. 4.2 Linear Transformations
    3. 4.3 Three Dimensions
    4. 4.4 Affine Transformations
    5. 4.5 Complements and Details
    6. 4.6 Exercises
  10. Chapter 5: Orientation
    1. 5.1 Cartesian Coordinate Systems
    2. 5.2 Cameras
    3. 5.3 Other Coordinate Systems
    4. 5.4 Complements and Details
    5. 5.5 Exercises
  11. Chapter 6: Polygons and Polyhedra
    1. 6.1 Triangles
    2. 6.2 Polygons
    3. 6.3 Polyhedra
    4. 6.4 Complements and Details
    5. 6.5 Exercises
  12. Chapter 7: Curves and Surfaces
    1. 7.1 Curve Descriptions
    2. 7.2 Bézier Curves
    3. 7.3 B-splines
    4. 7.4 Nurbs
    5. 7.5 Surfaces
    6. 7.6 Complements and Details
    7. 7.7 Exercises
  13. Chapter 8: Visibility
    1. 8.1 Viewing
    2. 8.2 Perspective Transformation
    3. 8.3 Hidden Surfaces
    4. 8.4 Ray Tracing
    5. 8.5 Complements and Details
    6. 8.6 Exercises
  14. Chapter 9: Lighting
    1. 9.1 Color Coordinates
    2. 9.2 Elementary Lighting Models
    3. 9.3 Global Illumination
    4. 9.4 Textures
    5. 9.5 Complements and Details
    6. 9.6 Exercises
  15. Chapter 10: Other Paradigms
    1. 10.1 Pixels
    2. 10.2 Noise
    3. 10.3 L-Systems
    4. 10.4 Exercises
  16. Appendix A: Geometry and Trigonometry
    1. A.1 Triangles
    2. A.2 Angles
    3. A.3 Trigonometric Functions
  17. Appendix B: Linear Algebra
    1. B.1 Systems of Linear Equations
    2. B.2 Matrix Properties
    3. B.3 Vector Spaces
  18. References
  19. Index
  20. End User License Agreement

Product information

  • Title: Mathematical Structures for Computer Graphics
  • Author(s): Steven J. Janke
  • Release date: November 2014
  • Publisher(s): Wiley
  • ISBN: 9781118712191