The Mathematical Basis of the UNIURF CAD System

The Mathematical Basis of the UNISURF CAD System deals with the mathematics involved in the use of the UNISURF CAD System. The book is divided into five chapters. Chapters 1 and 2 deal with the basic principles, expression of a point, and hodographs of curves and patches. Chapters 3 and 4 deal with the volume and parametric transformations of curves and patches, and Chapter 5 covers the general and special cases of blending. The text is recommended for mathematicians and designers who would like to know more about the mathematical aspect of the UNISURF CAD system.

Contents

Introduction

Geometric Elements

1 Curves

1.1 Basic Principle

1.2 Expression of A Point

1.3 Hodographs

1.4 Determination of A Characteristic Polygon

2 Patches

2.1 Basic Principle

2.2 Expression for a Point

2.3 Hodographs

2.4 Silhouette Lines

2.5 Determination of a Characteristic Net

2.6 Modification of a Patch

3 Volumes

3.1 Points

3.2 Curves

3.3 Patches

4 Parametric Transformations

4.1 Curves

4.2 Patches

4.3 Overall deformation

5 Blending

5.1 General case

5.2 Special cases

Conclusion

Bibliography