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Applied Geometry for Computer Graphics and CAD
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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 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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