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

Marshall, Duncan L.,Marsh, Duncan

ISBN 10: 1852330805 / ISBN 13: 9781852330804

Editore: Springer, 1999

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Titolo: Applied Geometry for Computer Graphics and ...

Casa editrice: Springer

Data di pubblicazione: 1999

Legatura: Paperback

Condizione: Good

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Riassunto:

Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). It summarizes the essential mathematical concepts, and 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; Bezier 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.

Dalla quarta di copertina:

Focusing on the manipulation and representation of geometrical objects, this book explores

the application of geometry to computer graphics and computer-aided design (CAD).

An introduction to transformations of the plane and three-dimensional space describes how objects can be constructed from geometric primitives and manipulated. This leads into a treatment of projections and the method of rendering objects on a computer screen by application of the complete viewing operation. Subsequently, the emphasis is on the two principal curve and surface representations, namely, Bézier and B-spline (including NURBS).

As in the first edition, applications of the geometric theory are exemplified throughout the book, but new features in this revised and updated edition include:

the application of quaternions to computer graphics animation and orientation;

discussions of the main geometric CAD surface operations and constructions: extruded, rotated and swept surfaces; offset surfaces; thickening and shelling; and skin and loft surfaces;

an introduction to rendering methods in computer graphics and CAD: colour, illumination models, shading algorithms, silhouettes and shadows.

Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and links to other useful websites.

Designed for students of computer science and engineering as well as of mathematics, the book provides a foundation in the extensive applications of geometry in real world situations.