Geometric Concepts for Geometric Design

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Overview

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

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Editorial Reviews

Booknews
Provides a solid foundation of applied geometry as used in geometric design and modeling, presenting ways to visualize a variety of geometric problems and the tools for their accurate representation. The discussions include linear algebra, images and projections, affine geometry, euclidean geometry, projective geometry, descriptive geometry, basic algebraic geometry, and differential geometry. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781568810041
  • Publisher: Taylor & Francis
  • Publication date: 7/1/1994
  • Pages: 424

Table of Contents

Preface
Notation
I Some Linear Algebra 1
1 Linear Systems
2 Linear Spaces
3 Least Squares
II Images and Projections 29
4 Parallel Projections
5 Moving the Object
6 Perspective Drawings
7 The Mapping Matrix
8 Reconstruction
III Affine Geometry 77
9 Affine Space
10 The Barycentric Calculus
11 Affine Maps
12 Affine Figures
13 Quadrics in Affine Spaces
14 More on Affine Quadrics
15 Homothetic Pencils
IV Euclidean Geometry 153
16 The Euclidean Space
17 Some Euclidean Figures
18 Quadrics in Euclidean Space
19 Focal Properties
V Some Projective Geometry 205
20 The Projective Space
21 Projective Maps
22 Some Projective Figures
23 Projective Quadrics
VI Some Descriptive Geometry 265
24 Associated Projections
25 Penetrations
VII Basic Algebraic Geometry 297
26 Implicit Curves and Surfaces
27 Parametric Curves and Surfaces
28 Some Elimination Methods
29 Implicitization, Inversion and Intersection
VIII Differential Geometry 351
30 Curves
31 Curves on Surfaces
32 Surfaces
Bibliography 389
Index 395
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