TABLE OF CONTENTS Most of us have studied geometry to some extent once, and in most cases, it was euclidean geometry. That geometry is perfectly adequate to handle objects such as points and lines, circles and planes, and much more. In fact, it is used successfully in the computer aided construction of cars, ships, and airplanes the process known as CAD, or Computer Aided Design.
As we shall see later, projective geometry is the natural setting for NURBS: many of their intrinsic properties are much easier understood in a projective context.
Euclidean geometry is an indispensable tool for some applications, but it has its shortcomings in other areas. If we are to deal with how we see things, the euclidean viewpoint becomes less advantageous. Looking up at high rise buildings, we perceive parallel lines as converging, and euclidean geometry can't cope with that. In projective geometry, there are no parallel lines it is therefore the geometry of choice for those working with perceived images. Architects use projective geometry when drawing a building as it would appear to an observer; computer graphics programmers use it when they model "realistic" scenes.
The roots of projective geometry go back to the late middle ages; and they were not in mathematics, but in the arts. Medieval painters neglected the concept of realistic perspective for religious reasons. It was the advent of the renaissance that led artists to study the techniques necessary for realistic rendering. Among them, we find names such...
