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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.
Features
Presents an easy-to-read introduction to computer graphics and geometric modeling
Delineates vector methods, mass points, affine and projective maps, and blossoming
Emphasizes high-level algorithms, including key curve/surface spline creation and manipulation algorithms
Uses an innovative approach by presenting turtles and fractals first
Provides formulas for transformations about planes and axes in arbitrary positions
Includes many exercises and programming projects
Offers a website with PowerPoint slides
Contents
I. Two-Dimensional Computer Graphics: From Common Curves to Intricate Fractals, 1. Turtle Graphics, 2. Fractals from Recursive Turtle Programs, 3. Some Strange Properties of Fractal Curves, 4. Affine Transformations, 5. Affine Geometry: A Connect-the-Dots Approach to Two-Dimensional Computer Graphics, 6. Fractals from Iterated Function Systems, 7. Fixed-Point Theorem and Its Consequences, 8. Recursive Turtle Programs and Conformal Iterated Function Systems, II. Mathematical Methods for Three-Dimensional Computer Graphics, 9. Vector Geometry: A Coordinate-Free Approach, 10. Coordinate Algebra, 11. Some Applications of Vector Geometry, 12. Coordinate-Free Formulas for Affine and Projective Transformations, 13. Matrix Representations for Affine and Projective Transformations, 14. Projective Space versus the Universal Space of Mass-Points, 15. Quaternions: Multiplication in the Space of Mass-Points, III. Three-Dimensional Computer Graphics: Realistic Renderin, 16. Color and Intensity, 17. Recursive Ray Tracing, 18. Surfaces I: The General Theory, 19. Surfaces II: Simple Surfaces, 20. Solid Modeling, 21. Shading, 22. Hidden Surface Algorithms, 23. Radiosity, IV. Geometric Modeling: Freedom Curves and Surfaces, 24. Bezier Curves and Surfaces, 25. Bezier Subdivision, 26. Blossoming, 27. B-Spline Curves and Surfaces, 28. Knot Insertion Algorithms for B-Spline Curves and Surfaces, 29. Subdivision Matrices and Iterated Function Systems, 30. Subdivision Surfaces. ISBN 9781439803349
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