Geometry for Computer Applications

1. Auflage 2026
ISBN: 978-1-041-31557-5
Verlag: Taylor & Francis Ltd

Buch, Englisch, 564 Seiten, Format (B × H): 178 mm x 254 mm

Reihe: Advances in Applied Mathematics

Geometry is a core part of modern technology. Geometry represented in computer systems is an essential element of numerous things in our lives -- the manufactured objects we use every day, every curve drawn on a phone or computer screen, every character 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 in a game or animation.

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 want to add a real-world flavor to calculus, linear algebra, differential geometry, or numerical analysis courses.

- Ambitious CAD system users who want to know how their systems work (and why they sometimes don’t), or want to implement add-on extensions.

- 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).

Some of the book is merely high-school coordinate geometry, presented from an industrial perspective, but 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 elementary calculus, but not much more.

The insights presented here are the product of nearly 50 years of insider industry experience.

Zielgruppe

Professional Practice & Development, Professional Training, and Undergraduate Advanced

Autoren/Hrsg.

Allen, George

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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

Über Autor(innen)

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 SIGGRAPH 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.