1. Motivation
2. Points and Vectors
3. Transformations
4. Matrices
5. Abstract Vector Spaces
6. Coordinates in 3D
7. Transformation Matrices
8. Equations and Representations
9. Simple Planar Curves
10. Tangents, Normals, and Curvature
11. Simple Curves in 3D Space
12. Simple Surfaces
13. Differential Geometry
14. Geometry Quality
15. Quadratic Curves
16. Rational Quadratic Curves
17. Cubic Curves
18. Simple Spline Curves
19. General Polynomial Curves
20. B-Spline Curves
21. B-Spline Basis Functions
22. Interpolation with Curves
23. Simple Free-Form Patches
24. Triangular Patches
25. General Tensor Product Surfaces
26. Rational Curves and Surfaces
27. Interpolation with Surfaces
28. Offset Curves and Surfaces
29. Approximation of Functions
30. Approximation of Curves
31. Approximation of Circular Arcs
32. Least Squares Fitting
33. Geometric Computations
34. Moments of Inertia
35. Homogeneous Coordinates
36. B-rep Solid Modeling
37. Implicit Modeling
Biography
George Allen has decades of experience in developing computer-aided design (CAD) software and in helping major corporations use it to improve their productivity. He is recognized worldwide as a leading expert in the field, both by academics and industry leaders. He led the development of several new technologies in the NX CAD software, especially in geometric design. His advice and guidance have served to improve productivity at some of the world’s largest manufacturing companies. Beyond his industrial work, George has taught a graduate course in CAD/CAM geometry at U.C. Irvine, and SIGRAPH courses on solid modeling. He holds a B. Sc. in Mathematics from the University of Sheffield, and an M. A. in Mathematics from the University of California.
