ABSTRACT

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.

part I|2 pages

Some Linear Algebra

chapter 1|10 pages

Linear Systems

chapter 2|8 pages

Linear Spaces

chapter 3|8 pages

Least Squares

part II|2 pages

Images and Projections

chapter 4|10 pages

Parallel Projections

chapter 5|7 pages

Moving the Object

chapter 6|11 pages

Perspective Drawings

chapter 7|12 pages

The Mapping Matrix

chapter 8|6 pages

Reconstruction

part III|2 pages

Affine Geometry

chapter 9|7 pages

Affine Space

chapter 10|13 pages

The Barycentric Calculus

chapter 11|8 pages

Affine Maps

chapter 12|13 pages

Affine Figures

chapter 13|11 pages

Quadrics in Affine Spaces

chapter 14|12 pages

More on Affine Quadrics

chapter 15|10 pages

Homothetic Pencils

part IV|2 pages

Euclidean Geometry

chapter 16|13 pages

The Euclidean Space

chapter 17|11 pages

Some Euclidean Figures

chapter 18|9 pages

Quadrics in Euclidean Space

chapter 19|17 pages

Focal Properties

part V|2 pages

Some Projective Geometry

chapter 20|14 pages

The Projective Space

chapter 21|10 pages

Projective Maps

chapter 22|16 pages

Some Projective Figures

chapter 23|18 pages

Projective Quadrics

part VI|2 pages

Some Descriptive Geometry

chapter 24|17 pages

Associated Projections

chapter 25|13 pages

Penetrations

part VII|2 pages

Basic Algebraic Geometry

chapter 26|11 pages

Implicit Curves and Surfaces

chapter 27|17 pages

Parametric Curves and Surfaces

chapter 28|10 pages

Some Elimination Methods

chapter 29|14 pages

Implicitization, Inversion and Intersection

part VIII|2 pages

Differential Geometry

chapter 30|13 pages

Curves

chapter 31|10 pages

Curves on Surfaces

chapter 32|13 pages

Surfaces