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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). 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.
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.