Geometric Tools for Computer Graphics

CHAPTER 4 MATRICES, VECTOR ALGEBRA, AND TRANSFORMATIONS

4.1 INTRODUCTION

The point of the preceding chapter was to introduce the concepts and principles of geometry in a coordinate-free fashion. For example, most treatments of the dot product simply describe it in terms of how you perform arithmetic on row and column matrices, without providing much in the way of an intuitive understanding or justification, whereas our approach was purely geometrical.

DeRose (1989, 1992) and Goldman (1985, 1987) strongly advocate this coordinate-free approach. DeRose describes a coordinate-free API, and an implementation is available. Such an approach has much to recommend it, especially in contrast to the more usual scheme of requiring programmers to explicitly ...