Mathematical Structures for Computer Graphics 1st Edition by Steven J Janke ISBN 1118712196 9781118712191

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ISBN 10: 1118712196 
ISBN 13: 9781118712191
Author: Steven J Janke

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.

Mathematical Structures for Computer Graphics 1st Table of contents:

• Chapter 1: Foundations of Geometry

  • Euclidean Geometry and Coordinate Systems

  • Vectors and Matrices

  • Transformations in 2D and 3D Space

  • Homogeneous Coordinates

• Chapter 2: Linear Algebra for Graphics

  • Vectors and Vector Spaces

  • Matrix Operations and Properties

  • Eigenvalues and Eigenvectors

  • Linear Transformations and Projections

• Chapter 3: Geometry in 2D and 3D

  • Points, Lines, and Polygons in 2D

  • 3D Points and Transformations

  • Curves and Surfaces: Parametric and Implicit Representations

  • Solid Modeling and Boundary Representation

• Chapter 4: Transformations and Coordinate Systems

  • Translation, Rotation, and Scaling

  • Affine Transformations

  • Perspective Projection and Camera Models

  • Viewing and Clipping in Graphics

• Chapter 5: Curves and Surfaces in Computer Graphics

  • Parametric Curves: Bézier, B-Splines, and NURBS

  • Surfaces: Parametric and Implicit Surfaces

  • Surface Interpolation and Approximation

• Chapter 6: Geometric Algorithms

  • Intersection of Lines and Curves

  • Convex Hulls and Voronoi Diagrams

  • Polygon Triangulation and Meshes

  • Computational Geometry Applications in Graphics

• Chapter 7: Rasterization and Scan Conversion

  • Pixel-based Representation

  • Line and Curve Drawing Algorithms

  • Filling Polygons and Anti-aliasing Techniques

  • Hidden Surface Removal

• Chapter 8: Lighting and Shading Models

  • The Mathematics of Light Interaction

  • Lambertian and Phong Shading Models

  • Normal Vectors and Surface Normals

  • Ray Tracing and Reflection Models

• Chapter 9: Color Theory and Representation

  • Color Models: RGB, HSV, CMYK

  • Color Spaces and Conversion

  • Applications of Color in Computer Graphics

• Chapter 10: Computational Models of 3D Rendering

  • Rasterization vs. Ray Tracing

  • Shading Techniques and Texturing

  • Global Illumination and Radiosity

  • Rendering Algorithms and Optimization

• Chapter 11: Geometric Modeling Techniques

  • Polygonal Modeling and Meshes

  • Subdivision Surfaces and Smooth Surfaces

  • 3D Texture Mapping and Mapping Techniques

  • Procedural and Parametric Modeling

• Chapter 12: Computer Graphics Algorithms

  • Numerical Methods in Graphics

  • Optimization Techniques in Rendering

  • Animation and Kinematics

• Chapter 13: Advanced Topics in Computer Graphics

  • Procedural Generation of Graphics

  • Physically-Based Rendering

  • Virtual Reality and Augmented Reality Models

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Tags: Steven J Janke, Mathematical Structures, Computer Graphics