Handbook of Computer Aided Geometric Design

Chapter 5

Rational Techniques

Hans J. Wolters

The following article will focus on rational parametric curves and surfaces and how they are used in geometric modeling applications. Aside from giving an overview of the state-of-the-art, I will emphasize the role of rational techniques in commercial CAD packages.

5.1 INTRODUCTION

Looking at the history of CAGD in industry, it can be argued that rational techniques and representations were at the root of geometric modeling. In particular conic sections and quadric surfaces were the initial building blocks of early CAD systems. Liming [27],[28] detailed many geometric constructions for aircraft design using conics. Later S. Coons at Ford introduced conics into a CAD system; independently conics ...