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.
Author(s): Sherif Ghali
Edition: 1
Publisher: Springer
Year: 2008
Language: English
Pages: 357
City: London
Tags: 3D; OpenGL; Design; Modeling; Polygon; Programming; Shading
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
