TABLE OF CONTENTS The ability to create geometric models of objects and to display and interact with them on a computer-graphics monitor has brought about a revolution in science, industry, and entertainment, too. Computer graphics applications now quickly and accurately generate images for medical diagnostic devices, entertain us with challenging computer games, and let us create special effects for movies. Computer graphics gives doctors, scientists, and engineers a new way to look at the world, producing images of phenomena beyond their power to visualize just a few years ago. This chapter introduces some of the basic geometry and mathematics of computer graphics, including display coordinate systems, windows and viewports, line and polygon clipping, geometric-element display, and visibility.
The most important characteristic of a coordinate system is the number of its dimensions. The simplest coordinate system is one dimensional, consisting of an unbounded straight line, a reference point O on it, called the origin, and a scale of measure, or metric. This is all we need to position, construct, and measure geometric objects, which in this one- dimensional system are limited to points and lines.
We locate a point p in this system by giving its distance x from the origin (Figure 17.1). This single number, a coordinate, describes and locates p. A plus or minus sign on x tells us which direction to measure from the origin. Mathematicians sometimes refer to this one-dimensional coordinate system as the real-number line, because there...
