Goldman An Integrated Introduction to Computer Graphics and Geometric Modeling

1. Auflage 2011
ISBN: 978-1-4398-0335-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 574 Seiten

Reihe: Chapman & Hall/CRC Computer Graphics, Geometric Modeling, and Animation Series

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.

Zielgruppe

Upper undergraduate/graduate students in introductory computer graphics/geometric modeling courses.

Autoren/Hrsg.

Goldman, Ronald

Fachgebiete

• Mathematik | Informatik EDV | Informatik Professionelle Anwendung
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

Two-Dimensional Computer Graphics: From Common Curves to Intricate Fractals
Turtle Graphics
Turtle Graphics
Turtle Commands
Turtle Programs

Fractals from Recursive Turtle Programs
Fractals
Looping Lemmas
Fractal Curves and Recursive Turtle Programs
Programming Projects

Some Strange Properties of Fractal Curves
Fractal Strangeness
Dimension
Differentiability
Attraction
Affine Transformations
Transformations
Conformal Transformations
Algebra of Affine Transformations
Geometry of Affine Transformations
Affine Coordinates and Affine Matrices
Conformal Transformations: Revisited
General Affine Transformations
Affine Geometry: A Connect-the-Dots Approach to Two-Dimensional Computer Graphics
Two Shortcomings of Turtle Graphics
Affine Graphics
Fractals from Iterated Function Systems
Generating Fractals by Iterating Transformations
Fractals as Fixed Points of Iterated Function Systems
Fractals as Attractors
Fractals with Condensation Sets
Programming Projects

Fixed-Point Theorem and Its Consequences
Fixed Points and Iteration
Trivial Fixed-Point Theorem
Consequences of the Trivial Fixed-Point Theorem
Programming Projects

Recursive Turtle Programs and Conformal Iterated Function Systems
Motivating Questions
Effect of Changing the Turtle’s Initial State
Equivalence Theorems
Conversion Algorithms
Bump Fractals
Programming Projects

Mathematical Methods for Three-Dimensional Computer Graphics
Vector Geometry: A Coordinate-Free Approach
Coordinate-Free Methods
Vectors and Vector Spaces
Points and Affine Spaces
Vector Products
Appendix A: The Nonassociativity of the Cross Product
Appendix B: The Algebra of Points and Vectors

Coordinate Algebra
Rectangular Coordinates
Addition, Subtraction, and Scalar Multiplication
Vector Products

Some Applications of Vector Geometry
Introduction
Trigonometric Laws
Representations for Lines and Planes
Metric Formulas
Intersection Formulas for Lines and Planes
Spherical Linear Interpolation
Inside-Outside Tests

Coordinate-Free Formulas for Affine and Projective Transformations
Transformations for Three-Dimensional Computer Graphics
Affine and Projective Transformations
Rigid Motions
Scaling
Projections

Matrix Representations for Affine and Projective Transformations
Matrix Representations for Affine Transformations
Linear Transformation Matrices and Translation Vectors
Rigid Motions
Scaling
Projections
Perspective
Programming Projects

Projective Space versus the Universal Space of Mass-Points
Algebra and Geometry
Projective Space: The Standard Model
Mass-Points: The Universal Model
Perspective and Pseudoperspective

Quaternions: Multiplication in the Space of Mass-Points
Vector Spaces and Division Algebras
Complex Numbers
Quaternions

Three-Dimensional Computer Graphics: Realistic Rendering
Color and Intensity
Introduction
RGB Color Model
Ambient Light
Diffuse Reflection
Specular Reflection
Total Intensity

Recursive Ray Tracing
Raster Graphics
Recursive Ray Tracing
Shadows
Reflection
Refraction

Surfaces I: The General Theory
Surface Representations
Surface Normals
Ray–Surface Intersections
Mean and Gaussian Curvature

Surfaces II: Simple Surfaces
Simple Surfaces
Intersection Strategies
Planes and Polygons
Natural Quadrics
General Quadric Surfaces
Tori
Surfaces of Revolution
Programming Projects

Solid Modeling
Solids
Constructive Solid Geometry
Boundary Representations
Octrees
Programming Projects

Shading
Polygonal Models
Uniform Shading
Gouraud Shading
Phong Shading
Programming Projects
Hidden Surface Algorithms
Hidden Surface Algorithms
The Heedless Painter
z-Buffer (Depth Buffer)
Scan Line
Ray Casting
Depth Sort
bsp-Tree
Programming Projects
Radiosity
Radiosity
Radiosity Equations
Form Factors
Radiosity Rendering Algorithm
Solving the Radiosity Equations
Programming Projects

Geometric Modeling: Freedom Curves and Surfaces
Bezier Curves and Surfaces
Interpolation and Approximation
de Casteljau Evaluation Algorithm
Bernstein Representation
Geometric Properties of Bezier Curves
Differentiating the de Casteljau Algorithm
Tensor Product Bezier Patches
Bezier Subdivision
Divide and Conquer
de Casteljau Subdivision Algorithm
Rendering and Intersection Algorithms
Variation Diminishing Property of Bezier Curves
Joining Bezier Curves Smoothly
Programming Projects

Blossoming
Motivation
Blossom
Blossoming and the de Casteljau Algorithm
Differentiation and the Homogeneous Blossom

B-Spline Curves and Surfaces
Motivation
Blossoming and the Local de Boor Algorithm
B-Spline Curves and the Global de Boor Algorithm
Smoothness
Labeling and Locality in the Global de Boor Algorithm
Every Spline Is a B-Spline
Geometric Properties of B-Spline Curves
Tensor Product B-Spline Surfaces
Nonuniform Rational B-Splines (NURBs)
Knot Insertion Algorithms for B-Spline Curves and Surfaces
Motivation
Knot Insertion
Local Knot Insertion Algorithms
Global Knot Insertion Algorithms
Programming Projects

Subdivision Matrices and Iterated Function Systems
Subdivision Algorithms and Fractal Procedures
Subdivision Matrices
Iterated Function Systems Built from Subdivision Matrices
Fractals with Control Points
Programming Projects

Subdivision Surfaces
Motivation
Box Splines
Quadrilateral Meshes
Triangular Meshes
Programming Projects

Further Readings
Index
A Summary and Exercises appear at the end of each chapter.

Über Autor(innen)

Ron Goldman is a professor of computer science at Rice University, Houston, Texas. Dr. Goldman’s current research interests encompass the mathematical representation, manipulation, and analysis of shape using computers.