What a great time to be alive!

That's how I felt after I saw a three-hour demo of the upcoming version of Lightwave 3D a couple of weeks ago. There were so many remarkable developments, so much easy, interactive power, that I could not help feeling proud about what artists and programmers are doing together to make 3-D art and animation accessible to a wide audience. The most extraordinary advancement, in my opinion, was a new kind of animation method I'd never seen (or even heard of) before. The demonstrator had created a simple keyframe animation--a head turning back and forth. Then, as a preview of this animation was running in a loop on the screen, he edited the animation, making the head nod up and down. He was actually editing the animation as it was running, interacting with the moving objects in real-time, and the application set the keyframes to conform to the movement of his mouse. Those with any experience at all in keyframe animation will understand at once how revolutionary this is.

I mention this not to hype Lightwave, though I think it is a very outstanding application. No doubt these same advancements will appear on many other applications as well. I note it rather to emphasize that 3-D technology is evolving at an astonishing pace--so quickly that much of what I write today will soon be out of date. The time to get involved is right now, just as powerful, fully professional tools are becoming available on affordable platforms. I noticed in today's newspaper that Intel has cut the price of a 200 MHz Pentium Pro in half in anticipation of their next microprocessor offering. Even a single 200 MHz Pentium Pro is enough for professional 3-D animation. Nor does one need a $1,000 video card to run OpenGL shaded previews (though it's nice to have one).

Let's turn to the topic of modeling.

Thus far in these tutorials, we have considered using the PRIMITIVES offered by the application, and then editing or deforming them to get the geometry we want. An enormous amount of modeling is possible from this approach. But often we must create even the basic geometry from scratch. This is one of the most creative aspects of 3-D graphics, both for the programmers developing the tools and for the artists using them. Think about it for a second. How would one go about creating 3-D objects in a virtual space, on a 2-D screen, using a mouse? When an artist models in clay, he or she shapes the physical object in true 3-D space using his or her hands. How can we put our hands into the virtual space behind our computer screen?

Every 3-D application handles modeling differently. One of the most important factors in choosing an application is comfort with the modeling tools. Some applications provide fabulous control in model building, at the cost of complexity. Other applications are easier to use and more intuitive, but may not provide as much control. Yet, underlying all of the different implementations are some very basic concepts. We will review these concepts in the following two parts of this tutorial.

But before we can do so, we must refine our understanding of a MODEL a little bit. Thus far, we have been describing a 3-D model as a mesh of polygons. We have learned (in Lesson 5) that using a polygon mesh does not prevent us from RENDERING smooth curving surfaces. Some applications, such as Lightwave 3D, model directly in polygons. All surfaces are treated as polygon meshes, even when they are being created and edited. But most applications have two different kinds of models. If a model involves smooth curving surfaces (such as a sphere), it is provisionally stored as a mathematical description of the curves. This makes it possible to edit curved shapes by manipulating curves, rather than pushing around points and polygons. However, each time the objects is rendered, the model is automatically converted to a polygon mesh that approximates the curved surfaces. This is necessary because almost all rendering engines still operate from points and polygons, rather than from curves. The procedure of converting to curved surfaces to polygon mesh approximations is called "tesselation," and can be visualized as wrapping a fisherman's net around a curved object. Tesselation of curved 3-D surfaces into polygons is exactly analogous to digitizing continuous tone images into a grid of pixels when using a scanner.

Applications that allow you to create and edit curved surfaces as true curves (rather than polygon meshes) are often said to be "spline-based." A spline is a basic type of curve that can be described by a mathematical expression, and the word "spline" is often used very generally and inaccurately.

With this refinement in our understanding of modeling software, we can consisder the basic concepts of modeling.