Applied Geometry For Computer Graphics And Cad - Softcover

Marsh, D.

Softcover

ISBN 10: 1852330805 ISBN 13: 9781852330804

Publisher: SPRINGER-VERLAG, 1999

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.

About this title

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.

Review

From the reviews:

a nice introduction to the foundations of applications of geometry to computer graphics and computer-aided design....A useful textbook.

Zentralblatt MATH

Mathematics students often ask where they can find a nice introduction to computer graphics and computer-aided design; professors have also been known to pose the same question. They will all find an answer here: Marsh’s book should guide them effectively and painlessly towards the applications of mathematics and geometry in graphics and CAD.

Computer-Aided Design 32 (2000)

From the reviews of the second edition:

"This is a mathematics textbook on the basics of the geometry involved in computer graphics and computer-aided design, written at an undergraduate level suitable for students of mathematics, computer science, and engineering. ... All of the book’s topics are presented in a clean and concise way, with nice illustrations and attention to both geometric ideas and practical issues of computing. ... This book would be useful for instructors who want a specific reference ... ." (Adam Coffman, Mathematical Reviews, 2005h)

"Images generated by a computer are ubiquitous, they are used in science, in engineering, and by the entertainment business. This textbook is an introduction to the mathematics behind these images. ... This exposition is intended for a broad audience with basic mathematical knowledge (vectors, matrices, calculus)." (P. Schmitt, Monatshefte für Mathematik, Vol. 151 (4), 2007)

“The title says it all. ... covers exactly what you would expect: theory and background for applying geometric techniques for visualization on a computer. ... This book is part of the SUMS (Springer Undergraduate Mathematics Series). The theory and applications are explained well, and moreover the text contains numerous examples, problems, and fully worked solutions. The book was written with students in computer science, engineering as well as of mathematics in mind ... .” (Pieter Audenaert, Bulletin of the Belgian Mathematical Society, 2007)

Edition details

• Publisher: SPRINGER-VERLAG
• Publication date: 1999
• ISBN 10: 1852330805
• ISBN 13: 9781852330804
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 304