In Lesson 1, we were introduced to the basics of 3D space and began to feel our way around. We passed quickly over the idea that the objects we create are composed primarily of points this space--that they are 3-D coordinates designated (x,y,z), for example (1,3,5) or (999,0,-222). This tutorial takes this concept deeper, as we learn to construct the simplest possible object out of points in 3-D space.

But before we go on, let's take a moment to consider an important issue.

The vast majority of people first approaching 3-D graphics are intimidated by the math and geometry concepts. This is especially true of artists. How much of this stuff do we really have to understand in order to create?

We have become accustomed to a sharp line drawn between the arts and the sciences, but this was not always the case. The great Renaissance artists were both artists and scientists, as they had to be to master their art. These great painters and sculptors learned anatomy from the dissection of corpses, alongside the medical students. But their purpose was not to learn medicine, but rather how to represent the human body in art. They studied the geometry of Euclid, and they built and experimented with devices to explore perspective. These inventions became our modern day camera centuries later, but the Renaissance artists were exploring the physics of sight for artistic rather than scientific reasons.

Now, at the birth of 3-D computer graphics as an artistic medium, those who wish to master the tools and produce the art must return to the spirit of the Renaissance masters who delved into every field they needed for their art, without fears or prejudices. In any case, mathematical ideas that may seem dry and forbidding can suddenly seem beautiful and exciting as they are used to create our 3-D art.

Back to our subject. The reader will remember the 3D axes created in Lesson 1.

We are looking at the origin (0,0,0) from above and somewhat over to the left so that we can see the whole scene unobstructed. The blue axis is the vertical one, called y. Positive y values are up and negative ones are down. Let's assume that our axes extend exactly 1 unit from the origin. Thus the point (0,1,0) is at the top end of the y (blue) axis, and (0,-1,0) is at the bottom end. Take a moment to be sure you can imagine this before you continue.

The yellow axis is the horizontal one, called x. (1,0,0) is at the right tip of this axis and (-1,0,0) is at the left tip as we look from the front. The green axis is z, the depth axis. (0,0,-1) is at the far end away from us, while (0,0,1) is at the tip nearest to us as we look from the front. Notice that depth increases in this way as the z value decreases. This creates what is called a "right-handed" coordinate system, and is the most common convention in use today.