Computer Graphics for Java Programmers, Second Edition

Chapter 5. Perspective

We now turn to the exciting subject of 3D graphics. As soon as we know how to compute the perspective image of a single point, we can easily produce more interesting images. To obtain the perspective image of a straight line, we simply connect the images of its endpoints, using the fact that the image of a straight line is also a straight line. In this chapter, the computation of the perspective image of a point is done in two steps: a viewing transformation followed by a perspective transformation.

INTRODUCTION

In Figure 5.1 a two-dimensional representation of a cube is shown along with some auxiliary lines. Although AB is a horizontal edge, it is not a horizontal line in the picture. Lines that in 3D space are horizontal and parallel meet in the picture in a so-called vanishing point. All these vanishing points lie on the same line, which is called the horizon. The horizon and vanishing points refer to the 2D image space, not to the 3D object space. For many centuries these concepts have been used by artists to draw realistic images of three-dimensional objects. This way of representing three-dimensional objects is usually referred to as perspective.

Figure 5.1. Vanishing points on the horizon

The invention of photography offered a new (and easier) way of producing images in perspective. There is a strong analogy between a camera used in photography and the human ...