Geometry for Computer Applications
Description
Geometry is a core part of modern technology. Geometry represented in computer systems forms an essential element of the manufactured objects we use every day--every curve drawn on a phone or computer screen, the first font on every printed page, every path followed by a robot, a CNC machine or a 3D printer, every structural or aerodynamic simulation, and every virtual world.
This book is written for:
¿ Curious Students of engineering, computer science, or applied mathematics needing a clear account of how the shapes of things can be represented in a computer system, and how geometry is actually used in industry.
¿ Dedicated Instructors who share the belief that this material should be taught.
¿ Ambitious CAD system users who want to know how the system works (and why they sometimes don't). More ambitious CAD users often want to enhance their systems by writing add-on tools requiring some knowledge of geometry.
¿ Practical Software engineers in need of solid reference materials.
The material should be useful to people developing CAD software, games, animation, graphics, simulation, and manufacturing systems (both subtractive and additive).
Most of the book is built on high-school coordinate geometry. The last few chapters discuss topics that will be new to many readers. Geometry can be explained with pictures; this book has hundreds of them to make advanced topics understandable. The reader will need to know some calculus, but not much more.
The author presents keys to a successful career. This book is the result of his long career in industry and a deep understanding of what professionals need to advance their own.
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Person
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.
Content
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