Function curves also allow you to edit the motion and location of every object in every frame of a shot. Let's say that you have animated a walk but you want to make the arms swing a little more quickly. Of course you could adjust every key frame by eye-balling the movement, but since the body is also moving, it can be difficult to see the exact differences as you make your changes. Therefore, it is easier to edit the shoulder's function curves instead. Each object or bone has curves associated with it that control the movement, rotation and scaling of it along the x, y and z axes. To increase the shoulder's rotation on certain frames, you simply adjust the position of the curve that represents the shoulder's rotation from front to back. Unfortunately, most programs don't allow you to use the function curves to edit the motion of an object, only the speed. This considerably increases the time required to animate a scene.

Hierarchies
The skeleton of a computer character is constructed as a hierarchy, where the first bone is known as a parent, and the bone connected to it is called the child. The upper arm is the child of the torso, but at the same time it is the parent to the lower arm, which is the parent to the hand and so on. The bone on the top of the hierarchy will in most cases be the pelvis, with the feet, hands and head at the bottom.

Inverse Kinematics
The problem with hierarchies is that movements can only translate down the hierarchy, not up. If you move the upper arm, the shoulder and hand will follow, since they are the children. However, if you move the hand, the rest of the arm will stay still because it doesn't react to the movements of its child. With inverse kinematics however, you can move the bone at the end of the hierarchy and make the rest of the body follow. This eliminates the computer animator's biggest problem, keeping a character's feet on the ground still as the pelvis moves. Without inverse kinematics the feet would be sliding around every time you move the pelvis or legs. With inverse kinematics you can lock the feet down in space and let the software keep them there.

Lights, Camera, Render!
Once the animation is completed, it has to be rendered. The computer analyses each frame and creates the final image, based on the information it has regarding the location of the models in the scene, the surface of the model and the lighting. At large production houses, technical directors take care of all of these aspects. Some create texture maps that are laid on the model, providing detail such as skin texture or fabric. They also decide how shiny or reflective each object should be. Others position all of the objects in the scene and compose shots using a virtual camera with real world parameters such as depth of field and focal length. Yet another technical director lights the scene, setting the position, direction, color and intensity of each light source. As with the camera functions, lighting in most 3D applications is designed to recreate lighting techniques in the real world. Needless to say, experience from related fields such as painting, cinematography, photography or stage lighting is an enormous advantage for a technical director, just as the ability to draw or sculpt is important for a modeler.

So, What Do I Use?
Unfortunately, only a very limited number of 3D applications offer the tools described in this article, as most programs are geared toward special effects, web design, flying logos or spaceships. Popular programs like Infini-D, ElectricImage, Strata StudioPro, Ray Dream Studio, or Truespace Caligari will not be of much help if character animation is all you care about.

By far the best programs available are Softimage 3D and Alias Power Animator, but these cost about $7000 and only run on very expensive Silicon Graphics and Windows NT workstations. In the medium price range, the big sellers are Lightwave 3D (for Macintosh, Silicon Graphics and Windows 95/NT) and 3D Studio/3D Studio MAX (Windows 95/NT), which cost $1500 and $3000 respectively.

If you want to concentrate solely on character animation, however, you're much better off financially with Martin Hash 3D Animation (available for Macintosh and Windows 95/NT), which offers all of the above tools for just $200! Its more expensive big brother is called Animation:Master, which offers more rendering and compositing features, but includes the same modeling and animation tools. To run version 4 of the program, the minimum requirement is a 100 MHz Power Mac or Pentium with at least 16 megabyte RAM, whereas version 5 requires 160 MHz and 32MB RAM. For 3D Studio and Lightwave 3D, you will need an even more powerful computer. Whereas you will probably have to sell your house, car, stereo and grandmother to afford to run Softimage or Alias.