Introduction to Geometric Computing

Preface.- Part 1 Euclidean Geometry.- 2D Computational Euclidean Geometry.- Points and Segments.- A Separate Type for Vectors.- Vector Normalization and Directions.- Affine Combinations.- Lines.- Vector Orthogonality and Linear Dependance.-Geomteric Predicates.- Predicate Return Type.- The Turn Predicate.- Side of Circle Predicate.- Order Predicate.- The Geometry of the Euclidean Line E1.- Immutability of Geometric Objects.- Exercises.- 3D Computational Euclidean Geometry.- Points in Euclidean Space.- Vectors and Directions.- Vector Orthogonality and Linear Dependance.- Planes in Space.- Lines in Space.- Sidedness Predicates in 3D.- Dominant Axis.- Exercises.- Affine Transformations.- Affine Transformations in 2D.- Properties of Affine Transformations.- Composition of Affine Transformations.- Affine Transformations Objects.- Viewport Mapping.- Orthogonal Matrices.- Orthogonal Transformations.- Euler Angles and Rotation in Space.- Rank of a Matrix.- Finding the Affine Mapping Given the Points.- Exercises.- Genericity in Geometric Computing.- Numerical Precision.- Part II Non-Euclidean Geometries.-??1D Computational Spherical Geometry.- 2D Computational Spherical Geometry.- Rotations and Quaternions.- Projective Geometry.- Homogenous Coordinates for Projective Geometry.- Barycentric Coordinates.- Oriented Projective Geometry.- Oriented Projective Intersections.- Coordinate-Free Geometry.- Homogeneous Coordinates for Euclidean Geometry.- Coordinate-Free Geometric Computing.-?? Introduction to CGAL.- Part IV Raster Graphics.- Segment Scan Conversion.- Polygon-Point Containment.- Illumination and Shading.- Raster-Based Visibility.- Ray Tracing.- Graphs.-Tree and Graph Drawing.-??Tree Drawing.- Graph Drawing.- Part VI Geometric and Solid Modeling.- Boundary Representations.- The Halfedge Data Structure and Euler Operators.- BSP Trees in Euclidean and Spherical Geometries .- Geometry-Free Geometric Computing.- Constructive Solid Geometry.-??Part VII Vector Visibility.- Visibility from Euclidean to Spherical Spaces.- Visibility in Space.- The PostScript Language.- OpenGL.- The GLOW Toolkit.- Bibliography.-Index