If we are going to do 3-D animation, we must develop an intuitive grasp of 3-D space on a computer. All 3-D software, from Alias on a Silicon Graphics workstation down to Ray Dream on a PC or a Mac, is precisely the same in this regard. Someone who is not truly comfortable navigating and visualizing in this environment cannot even begin to create. So where do we start?
Let's place a point on our screen.
Well, this is not really a point, but a little sphere, and here we have our first brush with the tension between pure geometry and physical reality that we are going to face (and feed off of) again and again. Einstein taught the remarkable truth that there is no such thing as a point in physical space without reference to some material object. Let's leave meditation on this topic to the physicists and the philosophically-inclined. But notice that our starting point must by symbolized by some physical object, typically a tiny sphere.
From this point, let's pull out a horizontal tube.
Then we add a vertical tube, perpendicular to horizontal one.
We are looking face-on at what could well be a simple 2-dimensional image. The only clue that we are working in a 3-D graphics application is in the subtle shading. Yet this shading could have been added by an artist, and indeed, the illusion of 3-D was already mastered centuries ago by the likes of Vermeer and many of the Renaissance painters.
So, let's add the third dimension--depth--by adding a new tube through the center point, perpendicular to both of the others.
The new tube is green, but we can barely see it because we are looking squarly at its end.
So let's change our point of view a little.
Now that's better! We have just jumped into 3-D space.
To get the real sense of working in 3-D space, we must have movement. We can rotate our object around the vertical pole.
Notice how this movement defines a kind of plane (a flat surface) created by the intersecting yellow and green poles. We can imagine a flat plane, and the blue pole sticking out perpendicular to it. A line sticking out of a plane in this perpendicular way is said to be the "normal" of the plane. It's not too soon to learn this important word. It's part of the basic vocabulary of the 3-D artist.
We have been rotating the vertical axis. Now let's try turning the green axis, our original depth axis.
And finally, the original horizontal axis.
Take some time to get accustomed to these three different rotations. Hold the three images simultaneously on one screen and let them sink slowly into to your soul or subconscious (or whatever word you're comfortable with). This is, in the simplest form, the pure magic of 3-D computer graphics.
We have been treating our little construction as a physical object, but now let's change our perception a bit. Let's treat the object as a reference that defines a 3-D space. The point at the intersection of the three axes is the center of our space. And each axis now defines a direction to use when placing real objects in the scene. We have created a 3-D COORDINATE SPACE.
To make it clearer that the structure is now just the reference that defines our space, we'll change it all to white.
Let's place an object in our space. A red cube is set right at the center, with all its sides square to the white axes.
Next we rotate the cube around the vertical axis. Notice that our reference structure stays constant while the cube turns.
Take a deep breath, because this is a big step. What if the space itself rotated, taking the cube with it?
The space rotating? What could that mean? But the idea that we can move the space, meaning the reference by which all the objects in our space are located, is a very important idea to grasp right away in 3-D animation. It doesn't seem to make any difference here, but what if we move the cube away from the center of our space?
Now we clearly see the difference between rotating the cube and rotating the entire 3-D coordinate space in which the cube is placed. Clever, huh?
Notice something new as well. We not only moved the cube, but shrunk it. We manipulate objects in 3-D coordinate space by moving (translating), rotating, and resizing (scaling)them. These three processes together are called TRANSFORMATION.
Finally, we get rid of the white axes, which were only for our use in constructing the little animation, and we see the final result--the red cube in eternal orbit.
There's quite a bit to ponder here, certainly enough for a start. In the next lesson we'll learn to create a simple object.