Download PDF Introduction to Geometric Computing by Sherif Ghali

Sinopsis

Consider that we are about to embark on the design and implementation of a software system that has a geometric component. We decide to take a longterm look and to craft a set of geometric classes with enough care so that there would be a high likelihood that we reuse the classes in the next project we tackle. This chapter discusses the decisions that need to be made when designing a set of classes for points, lines, and other objects in planar Euclidean geometry.

Since the geometry tackled is familiar, there is little need to formalize the properties of the Euclidean plane and space. Although the details for designing classes for Euclidean geometry in the plane are quite simple, it is instructive to go through these details, partly because it will then be easier to appreciate the need for more complex structures, but also because doing so has the parallel benefit of acting as a review of C++. It is clear, for example, that we need classes for a point, a line, and a segment and that Cartesian coordinates will be used.

Content

1. 2D Computational Euclidean Geometry
2. Geometric Predicates
3. 3D Computational Euclidean Geometry
4. Affine Transformations
5. Affine Intersections
6. Genericity in Geometric Computing
7. Numerical Precision
8. 1D Computational Spherical Geometry
9. 2D Computational Spherical Geometry
10. Rotations and Quaternions
11. Projective Geometry
12. Homogeneous Coordinates for Projective Geometry
13. Barycentric Coordinates
14. Oriented Projective Geometry
15. Oriented Projective Intersections
16. Homogeneous Coordinates for Euclidean Geometry
17. Coordinate-Free Geometric Computing
18. Introduction to CGAL
19. Segment Scan Conversion
20. Polygon-Point Containment
21. Illumination and Shading
22. Raster-Based Visibility
23. Ray Tracing
24. Tree Drawing
25. Graph Drawing
26. Boundary Representations
27. The Halfedge Data Structure and Euler Operators
28. BSP Trees in Euclidean and Spherical Geometries
29. Geometry-Free Geometric Computing
30. Constructive Solid Geometry
31. Visibility from Euclidean to Spherical Spaces
32. Visibility in Space

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