An integrated introduction to computer graphics and geometric modeling. (2009)

• Record Type: Book
• Further Information: Note: Ronald Goldman.
• Other Names: Goldman, Ron, 1947-
• Contents: 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&
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2009
• Extent: 1 online resource (574 pages), (399 illustrations)
• Subjects: 006.6; Computer graphics; Three-dimensional display systems; Curves on surfaces -- Mathematical models
• Languages: English
• ISBNs: 9781439803356; 1439803358
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.