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内容説明
Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). 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, 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.
Book Description
The main aim of this book is to introduce geometry from the very basics and to progress to a level where the reader will have a full working knowledge of the subject and its applications. The subject matter consists 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 represented 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 describe the two most important representations of geometric objects in CAD packages; Bzier and B-spline curves. Curve and surface design and manipulation are described in detail, Casteljau and de Boor algorithms are derived and applied. The final chapter then develops the concept of curvature for curves and surfaces which is used to assess the quality of surfaces in design.
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