An Integrated Introduction to Computer Graphics and Geometric Modeling

✍ Scribed by Ronald Goldman

• Publisher: CRC Press
• Year: 2009
• Tongue: English
• Leaves: 592
• Series: Chapman & Hall/CRC Computer Graphics, Geometric Modeling, and Animation Series
• Edition: 1
• Category: Library

✦ Synopsis

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with fractals, rather than the typical line-drawing algorithms found in many standard texts. He also brings the turtle back from obscurity to introduce several major concepts in computer graphics.

Supplying the mathematical foundations, the book covers linear algebra topics, such as vector geometry and algebra, affine and projective spaces, affine maps, projective transformations, matrices, and quaternions. The main graphics areas explored include reflection and refraction, recursive ray tracing, radiosity, illumination models, polygon shading, and hidden surface procedures. The book also discusses geometric modeling, including planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, constructive solid geometry, boundary files, octrees, interpolation, approximation, Bezier and B-spline methods, fractal algorithms, and subdivision techniques.

Making the material accessible and relevant for years to come, the text avoids descriptions of current graphics hardware and special programming languages. Instead, it presents graphics algorithms based on well-established physical models of light and cogent mathematical methods.

✦ Table of Contents

Front cover
Contents
Foreword
Preface
Author
Part I: Two-Dimensional Computer Graphics: From Common Curves to Intricate Fractals
Chapter 1. Turtle Graphics
Chapter 2. Fractals from Recursive Turtle Programs
Chapter 3. Some Strange Properties of Fractal Curves
Chapter 4. Affine Transformations
Chapter 5. Affine Geometry: A Connect-the-Dots Approach to Two-Dimensional Computer Graphics
Chapter 6. Fractals from Iterated Function Systems
Chapter 7. The Fixed-Point Theorem and Its Consequences
Chapter 8. Recursive Turtle Programs and Conformal Iterated Function Systems
Part II: Mathematical Methods for Three-Dimensional Computer Graphics
Chapter 9. Vector Geometry: A Coordinate-Free Approach
Chapter 10. Coordinate Algebra
Chapter 11. Some Applications of Vector Geometry
Chapter 12. Coordinate-Free Formulas for Affine and Projective Transformations
Chapter 13. Matrix Representations for Affine and Projective Transformations
Chapter 14. Projective Space versus the Universal Space of Mass-Points
Chapter 15. Quaternions: Multiplication in the Space of Mass-Points
Part III: Three-Dimensional Computer Graphics: Realistic Rendering
Chapter 16. Color and Intensity
Chapter 17. Recursive Ray Tracing
Chapter 18. Surfaces I: The General Theory
Chapter 19. Surfaces II: Simple Surfaces
Chapter 20. Solid Modeling
Chapter 21. Shading
Chapter 22. Hidden Surface Algorithms
Chapter 23. Radiosity
Part IV: Geometric Modeling: Freedom Curves and Surfaces
Chapter 24. Bezier Curves and Surfaces
Chapter 25. Bezier Subdivision
Chapter 26. Blossoming
Chapter 27. B-Spline Curves and Surfaces
Chapter 28. Knot Insertion Algorithms for B-Spline Curves and Surfaces
Chapter 29. Subdivision Matrices and Iterated Function Systems
Chapter 30. Subdivision Surfaces
Further Readings
Index
Back cover