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

Marsh, Duncan, Marshall, Duncan L.

ISBN 10: 1852330805 / ISBN 13: 9781852330804

Published by Springer, 1999

About this Item

Seller Inventory # Abebooks464726

Bibliographic Details

Title: Applied Geometry for Computer Graphics and ...

Publisher: Springer

Publication Date: 1999

Binding: Paperback

Condition: New

About this title

Synopsis:

The main aim of this book is to introduce geometry from the very basic's and to progress to a level where the reader will have a full working knowledge of the subject and its applications. The subject matter con sists of two main threads: the manipulation and the representation of geometric objects. It begins by considering simple objects consisting of points and lines, followed by a description of how points may be re presented by homogenous coordinates, and how lines may be represented by line coordinates. Transformations are explained and it is shown how they are used to manipulate objects. The text then goes on to describ e the two most important representations of geometric objects in CAD p ackages; Bzier and B-spline curves. Curve and surface design and manip ulation are described in detail, Casteljau and de Boor algorithms are derived and applied. The final chapter then develops the concept of cu rvature for curves and surfaces which is used to assess the quality of surfaces in design.

From the Back Cover:

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.