Geometry for Computer Applications

This book explores how geometry in computer systems forms an essential element of the manufactured objects we use every day. For students of engineering, computer science, and applied mathematics, as well as instructors, CAD system users and practical software engineers.

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.