Introduction to Geometric Computing

✍ Scribed by Sherif Ghali

• Publisher: Springer
• Year: 2008
• Tongue: English
• Leaves: 338
• Edition: 1
• Category: Library

✦ Synopsis

Computing is quickly making much of geometry intriguing not only for philosophers and mathematicians, but also for scientists and engineers. What is the core set of topics that a practitioner needs to study before embarking on the design and implementation of a geometric system in a specialized discipline? This book attempts to find the answer. Every programmer tackling a geometric computing problem encounters design decisions that need to be solved. This book reviews the geometric theory then applies it in an attempt to find that elusive "right" design.

✦ Table of Contents

Front Matter
Pages i-xvii

Euclidean Geometry
    2D Computational Euclidean Geometry
    Pages 3-15

    Geometric Predicates
    Pages 17-25

    3D Computational Euclidean Geometry
    Pages 27-34

    Affine Transformations
    Pages 35-50

    Affine Intersections
    Pages 51-60

    Genericity in Geometric Computing
    Pages 61-68

    Numerical Precision
    Pages 69-83

Non-Euclidean Geometries
    1D Computational Spherical Geometry
    Pages 87-92

    2D Computational Spherical Geometry
    Pages 93-100

    Rotations and Quaternions
    Pages 101-108

    Projective Geometry
    Pages 109-118

    Homogeneous Coordinates for Projective Geometry
    Pages 119-142

    Barycentric Coordinates
    Pages 143-147

    Oriented Projective Geometry
    Pages 149-156

    Oriented Projective Intersections
    Pages 157-168

Coordinate-Free Geometry
    Homogeneous Coordinates for Euclidean Geometry
    Pages 171-174

    Coordinate-Free Geometric Computing
    Pages 175-181

    Introduction to CGAL
    Pages 183-190

Raster Graphics
    Segment Scan Conversion
    Pages 193-200

    Polygon-Point Containment
    Pages 201-204

    Illumination and Shading
    Pages 205-208

    Raster-Based Visibility
    Pages 209-212

    Ray Tracing
    Pages 213-215

Tree and Graph Drawing

    Tree Drawing
    Pages 219-226

    Graph Drawing
    Pages 227-234

Geometric and Solid Modeling

    Boundary Representations
    Pages 237-244

    The Halfedge Data Structure and Euler Operators
    Pages 245-253

    BSP Trees in Euclidean and Spherical Geometries
    Pages 255-264

    Geometry-Free Geometric Computing
    Pages 265-276

    Constructive Solid Geometry
    Pages 277-283

Vector Visibility

    Visibility from Euclidean to Spherical Spaces
    Pages 287-291

    Visibility in Space
    Pages 293-295

Back Matter
Pages 299-340

✦ Subjects

3D; OpenGL; Design; Modeling; Polygon; Programming; Shading