Applied Geometry for Computer Graphics and CAD

  • Authors
  • Duncan Marsh 

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Duncan Marsh
    Pages 1-18
  3. Duncan Marsh
    Pages 67-94
  4. Duncan Marsh
    Pages 95-134
  5. Duncan Marsh
    Pages 135-160
  6. Duncan Marsh
    Pages 161-186
  7. Duncan Marsh
    Pages 187-223
  8. Duncan Marsh
    Pages 225-266
  9. Duncan Marsh
    Pages 267-296
  10. Duncan Marsh
    Pages 297-343
  11. Back Matter
    Pages 345-350

About this book


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.


algorithms animation computer algebra computer graphics computer-aided design (CAD) construction rendering shading

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London 2005
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-85233-801-5
  • Online ISBN 978-1-84628-109-9
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site
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