Introduction to Geometric Computing
Book information
Description
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. 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
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