Applied Geometry for Computer Graphics and CAD: With Applications to Computer Graphics (Springer Undergraduate Mathematics Series)

Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). Following a summary of essential mathematical concepts, the book covers the representation of points, lines and transformations. A treatment of how transformations can be used to manipulate objects leads into the method of rendering objects on a computer screen by application of the complete viewing pipeline. Subsequently, the main emphasis is-on the two principal curve representations used in CAD packages and in computer graphics, namely, Bézier and B-spline curves. Over 260 exercises are included, many of which encourage, the reader to implement the techniques and algorithms discussed through use of a computer package with graphing and computer algebra capabilities. Suitable for students of engineering and computer science as well as of mathematics, the book provides a foundation in the extensive applications of geometry in real world situations.