Three-Axis Animation

Introduction

3D game character animation is a relatively new craft. Four years ago we would not have dreamed of animating facial expressions in real time, and now the latest line of video cards and consoles brings even more complexity to what we can do. The time has come to start reflecting on 3D game animation as a craft by defining the methods we use, establish some rules, find tricks, and understand what it takes to be a game animator. It is time to go from tinkering to crafting.

This article deals with the real time, in-game character animation, however, it is also useful to many people who are involved with animation in general. I explain and discuss the very basic rules of what I call three-axis animation, and present the essence of what I have learned during the past few years. Every animator has a different approach to the same problems, but I feel my experience could be helpful to some of you, especially if you are totally new to in-game animation.

What's the big deal?

You probably remember the little sixteen by sixteen blocks of pixels creating sprites that were supposed to look and act like characters with personality in a 2D game environment. Moving pixels around in 2D animation involves creating a blurry illusion of something, while animating in 3D is close to reproducing an actual motion with all its cold mathematical strangeness: acceleration, deceleration, forces, dynamics, weights and curves. Going 3D is a huge and frightening step forward. For a 2D animator, it's a strange new world. I started, like everybody else, using the 2D method of defining a few extreme key frames from a side view, and hoping it would work. Unfortunately, it did not work, mainly because 2D is an illusion in an impossible flat world and is accepted by the player (your average Joe player) as an illusion. In contrast, 3D implies a world that obeys the same laws as ours, in a world that is truly believable. Sure Mario can hop and jump without even moving his legs in a flat universe, but in a world with dimensions and space, everybody expects him to act and react according to physical laws. The difference between 2D and 3D is not an added dimension, but a heightened expectation from the player. That's the big deal!

Now, as animators, we can ignore this fact, and still try to fix some little animations, or we can rethink our ways of animating from the ground up. That means leaving behind everything we learned from 2D, and understanding exactly what we are doing.

Gravity is the key

Let me define the technical basics of what 3D animation exactly is. As I said earlier, in a believable universe we have to consider laws of nature. The main law that directly affects any movement in a believable universe is gravity. Every motion in a 3D space either is created by gravity or is a reaction to gravity. For example, you are probably sitting while reading this article. Try to stand up and visualize what keeps you standing. Mostly, it is the muscles in your legs (especially the thighs), and possibly the muscles in your arms if you are using the table to lift you up, that produce a force strong enough to counterbalance the effect of gravity. The creation of a force is the basis for motion in a 3Dspace.

However dry this topic may sound, bear with me, because understanding the basics often makes the difference between good and bad animations. If you keep in mind that your character has to create a force to counterbalance the effects of gravity every time you want to move it, you will avoid many common mistakes.

What does it really mean? A quick example can illustrate my point. If you want to have a standing character going from point A to point B, you have two ways of solving the problem:

In the first solution, you are creating the illusion of movement. The second solution illustrates a true comprehension and reproduction of the way physical laws create a movement. Some people will disagree with this because it makes inverse kinematics invalid. The truth is, inverse kinematics is a bit of a monster. Making a character walk by moving its feet is wrong; it is the total opposite of a natural walk to imply that the feet are moving because the legs are moving. Rather, it is simulating a motion, instead of reproducing a motion, and trying to create an effect without knowing what forces produce it. You should be only interested in knowing what make things move, because if you understand what you do, you can control it.

Gravity, and how it is used to create movement, is the first rule of three-axis animation. The two other rules are balance, tilt and twist. Let me explain to you how those rules are tied together and can be used to create a complex animation.

Out of balance

I already said that every motion is related to gravity and, in a way, created by it. Actually, it is known as being in balance or out of balance. Almost every move starts by putting the body out of balance and ends by regaining balance before falling down. To explain this, let me try to define two very important concepts: the center of gravity, and the idea of balance.
The center of gravity is a point situated between the hips (higher or lower depending on the body mass). This center of gravity is usually the first bone or root point of a character skeleton. To move the body, the limbs have to alter the position of the center of gravity.

A body is in balance when you can trace a vertical line from the pit of the neck (upper torso) to the ankle of the supporting foot (if the character is supporting his weight on one leg), or to a line that joins the two ankles (if the character is supporting his weight equally with his two legs). If this line is not perfectly vertical, the body is out of balance. You will notice that the center of gravity can be positioned anywhere in relation to that line. The only important points are the pit of the neck and the ankles. The amount of unbalance is relative to the angle of the line. The body is more likely to fall if the angle between the body and the ground is increased

The human walk is a great example to illustrate these two concepts and show how they are related. When starting from a standing position, (assuming our subject is right handed) the first movement of the walk is the forward rotation of the right leg around the hipbone, lifting the right foot up in front of the body. At the same time, the left leg rotates around the knee (the thigh is almost locked in place, the calf muscles produce all the force), and the left foot follows by rotating around the ankle. The body pushes forward as a result of the left leg rotation, and since the right foot is not in contact with the ground at that moment, the center of gravity is displaced. The whole body moves forward. This forward movement suddenly stops when the center of gravity passes in front of the supporting left leg (the balance line is no longer vertical). The body becomes out of balance and falls forward. This is when the right leg makes contact with the ground, and becomes the supporting leg and stops the fall. The body continues its forward motion. The whole movement repeats, however, this time the right leg is producing the forward thrust and the left leg is lifting to catch the fall. A walk is a succession of pushes and near falls, putting the body alternatively out of balance and in balance. We are using the effects of gravity to move our body mass on a linear path, with our legs simultaneously producing the thrust force and support. A walk is basically just a succession of controlled falls.

As you can see, trying to animate a walk, without knowing that you have to move the center of gravity by putting the body out of balance, is very difficult. If you do not know why each part of the body moves, you cannot understand how they move.

The good news is that there is an easy rule to remember: every movement of the body is based on a thrust (from the calves, thighs, arms, etc.), moving the center of gravity out of balance, and then a catch by a leg or an arm, putting the body back in balance.

The amount of thrust and the time between the thrust and the catch, determine the amplitude of the movement. Of course the more nimble the character is, the more extreme his movements will be. Moving a body means playing with gravity and playing with balance. If you remember that rule before starting any animation, you will have more control on what you can create.

Let's do the Twist

Now, there is obviously more complexity in a motion than just some muscles thrusting a body forward in space and trying to avoid a fall. Why is movement so complex? For the very simple reason that the body of every vertebrate is rigid. That can sound strange if you consider all the stretching and moving muscles that comprise most of our body, but the underlying structure is a rigid skeleton made of solid bone. Even an insect has a solid exoskeleton that makes its body rigid. Gravity, the most basic law of nature, has created the need for a rigid structure like the human skeleton for support.

Every movement we make is a rotation of several rigid bones around articulations. As far as game animation is concerned, there is no flexibility whatsoever in the skeleton. This is why you can animate a stick figure and still create a valid animation. Muscles are built over the skeleton, and their only function is to create the rotation of the rigid parts. Muscles create the force. Evolving big muscles has always been difficult for any living being, because it is a complex and very expensive piece of body hardware. Muscle also consumes a lot of energy to function properly. This is why our bodies have just enough muscle to allow us to move around. A simple increase in weight slows us tremendously. Animals have a rigid skeleton, and because they do not have extremely powerful muscles, they had to come up with a strategy, called the tilt and twist method, to allow them to move as fast as possible.

To illustrate this, let me go back to the human walk example. We have seen that the first movement of the walk is the forward rotation of the right leg around the hipbone, lifting the right foot up in front of the body. Now if you stand up and try to perform this by only using your thigh muscles to move the leg forward, you immediately realize one thing, your foot is sliding on the ground. There is nothing wrong with that, except that sliding a foot actually requires more effort than lifting it up. You will also realize you are almost out of balance, and it is difficult to stand straight.

So how can you actually lift your leg? You can do it only by tilting your hipbone to the left. Again, try to move your leg by tilting the hips and you will understand that this is what you do naturally. The tilting of the hipbone has two effects. First, it makes your right leg higher than the left one, thus allowing rotation forward without having your foot scraping the ground. Second, it moves your center of gravity over your left leg (the vertical line drawn from the pit of the neck to the ground is moving from between your feet to your left foot).With one easy tilt, we create a solution to two problems: you can lift your right leg and stay in balance. Of course, the balance is only on a lateral plane; we want to move forward. Therefore, the necessary unbalance I discussed earlier has to be created forward and not sideways.

Unfortunately, the tilting of the hips produces a different unbalance between the upper and lower parts of the body. Now that one leg is higher than the other, and the body weight is moving to the left, we have to compensate that motion with the top of our body. This is why we have to tilt our shoulders in the opposite direction of the hips with the right shoulder being higher than the left. Because this unbalance is minor, the tilt of our shoulders is at a smaller angle than the tilt of our hips. To stay level with the ground, the head is also tilted slightly in the opposite direction (same direction as the hips), as a result of the shoulders tilting.

As you can see, this very simple first step in the walk suddenly puts in motion not only the legs, but also the hips, shoulders, spine, and the head. What may appear very simple in a 3D program (just rotate one object around one pivot point), actually requires rotations on many other parts of the skeleton. By understanding that, you start to understand the underlying principle of three-axis animation: every part of the body has to move in three dimensions to create a realistic movement.

Tilting is a very effective and cost efficient way (in term of energy) to quickly rotate the parts of a skeleton, but living in a three-dimensional universe allows us to improve this efficiency with twisting. We have seen how the process of lifting our right leg for this crucial first step involves a rotation forward (Z-axis rotation) and the tilting of the hips (X-axis rotation). What about the Y-axis rotation?

When we move our right leg forward, we can easily improve the reach of the first step by simply rotating the hips on the Y-axis, twisting the lower part of the body to move the right hip forward. This is a very simple and small motion, but being at the top of the rotating leg, it gives a significant increase in reach. As in tilting, the same unbalance occurs with the top of the body. We have to twist the shoulders in the opposite direction of the hips to keep the body in balance. The head will also have to twist a little in the same direction as the hips.

The twisting motions of the body are designed to give more amplitude to any motion, while at the same time being very energy efficient. In addition, you discover that a number of movements are being improved in reach and ease by subtle twists at the main articulations (hips, thighs, shoulders and spine bones). The amount of twisting in a body is only limited by the physiology of an organism. For example, lizards and crocodiles have a very flexible spine, which allow them to twist in an extreme way to give more reach to their short legs. In humans, females have wider hipbones, which allows them a lot more twisting and tilting. To understand how an animal moves, you have to know the structure of the skeleton and where the main muscles are located. With a little training, and by simply observing a skeleton, you should be able to figure out the way a creature moves (especially if you want to animate dinosaurs, aliens and weird creatures).

Tilting and twisting is the last rule you have to understand to create any kind of animation. Every part of the body involved in creating a motion has to rotate on the three axes (X, Y, Z) at the same time. Because of gravity and the need to stay in balance, we vertebrates, have evolved this way of moving by rotating, tilting and twisting our rigid skeleton in the most efficient manner. Evolution plays a huge role in our movement. Centuries of trial and error have shaped muscles and bones to allow them freedom of movement and efficient management of energy. Learn this and understand it. Character animation is not a random process, because there is an underlying order and explanation for every part of a movement.

Creating

The rules of three-axis animation are extremely effective mainly because of their versatility. Every vertebrate moves according to these rules, even the ones without legs (like snakes).
For example, as a dog runs, it moves its center of gravity forward by pushing on its back legs (where its most powerful muscles are), slightly tilting the hips and shoulders but twisting them to cover more distance. This exaggerated twisting explains why the front paws of a dog hit the ground one after another instead of at the same time.

A monkey jumping from branch to branch observes the same rules. Obviously, it uses only its arms to move, but its arm muscles are not powerful enough to move fast, so it has to use a combination of extreme tilting and twisting in the shoulders to cover more distance with minimum effort.

How do I know all this? I didn't spend hours observing dogs or chimps in their natural habitat. I simply tried to understand why they move that way, and what is the most efficient way. The three axis animation principles are guidelines to analyze any kind of motion. Knowing that you can replicate about any movement by understanding it, gives you the freedom to invent new ones. The true challenge for an animator is obviously not to do a run cycle, but to come up with that crazy out of this world movement that your producer needs for his new fighting game. Games are not always realistic (not realistic as in cartoony), and you often need to create something bigger than life (like in any good kung fu movie), so you will have to invent a lot of moves. Inventing is challenging, but if you follow the basic rules, you can create something fantastic and believable.

Rules are better than tricks when you animate. They can apply to any kind of animation, and a basis to elaborate, create and give style to your work. Try to keep them in mind, and your life as a game animator will be a lot easier.

It's just a game

Now we have all the tools necessary to create the right animation for our character, but we have one last obstacle: remembering it's just a game. Animating for a game requires restrictions; from the number of polygons the character is made of, the ridiculously limited number of bones you can animate, to the numbers of key frames you are allowed for each movement. Restrictions are the ugly reality of game animation. If I tell you to animate a guy hitting the perfect hook on the jaw of his opponent, you will probably have no difficulty figuring it out. Now, if I tell you to animate it in twelve frames (almost a third of a second), you start to realize the real challange. There is no easy way to deal with restrictions in games, however, a few guidelines are useful. If you keep in mind the basic rules of three-axis animation, you can easily tweak, adapt, and simplify your animations without changing them.

The most important thing to keep in mind is how your animations will be seen, and not how they look. Seeing an animation in a 3D program is very different from seeing it in a game. This may seem obvious, but it is too often forgotten. If you are working on a fighting game for example, the camera will be very close and probably always on the side of your character. If you are working on a first person shooter, chances are the only thing the player will really see, are the death animations of his enemies. If you are working on a strategy title, the overhead camera will flatten and change every animation. This requires you to look at all your animations from the perspective of the player. Try to place the camera at the same angle as the game camera. Do not play your animations in slow motion or frame by frame. Think of it as a whole, rather than getting lost in useless details and minute tweaks that nobody but you can see. Game animation is an illusion and a craft, not a science.

The first thing about an animation is making it right. The second thing to remember is to make it interesting. This is why you have to know what part of your animation will be seen in the game. Put the subtle details in place, the key frames and the nicely crafted weight effects where you are sure they will be seen. Remember, if the player can't see them, they do not exist, and all of your work has been a complete waste of time

Try to make your animations simple and expressive. Making it right, does not mean you have to make it complex. The basic rules of movement tell us that every motion has to be cost efficient. Try to do the same for each animation. Do not create key frames all over the place, because you will have to correct every little glitch. Keeping it clean and simple will make it easier to manage.

Finally, basic rules give you basic animations. Remember, that the rules of three-axis animation are only a foundation to create, experiment, and discover. A memorable animation is one that adds to the character. You have to understand the how in animation, to be able to create the why. For instance, this guy is walking by thrusting his legs, and tilting and twisting his hips and shoulders, but why does he want to walk? What do I want to communicate with my animation? Just try to communicate one simple feeling. The guy is a guard who is alone in a room, and is probably bored and tired. Try to express the guys feeling of boredom through your animation. The player will remember he saw a person who shuffled around and looked believably bored, not just a mindless robot. This will give the player more information and enjoyment from the game world.

Rules are useful, and necessary, but they can become a distraction when the only thing you want is the right animation. Do not get obsessed with what is necessary to make it perfect. The animator should strive for the good animation that is imbued with emotion giving life to a mathematical object made of polygons.

Conclusion

The rules of three-axis animation are a simple way of understanding how a body moves, fights and uses gravity to stay in balance, tilting and twisting its limbs to achieve the greatest possible range with ease with each moving part of a skeleton rotating on the three axes at the same time to help create the motion. These rules are a base that allows greater control and freedom to create. Try to learn them, understand them, and then forget them.

If you want more information, you can read the following books:

Bridgman's Life Drawing by George B. Bridgman - Dover

The Human Figure in Motion by Eadweard Muybridge - Dover

Cyclopedia Anatomicae by Gyorgy Feher - Black Dog & Leventhal Publishers

The Illusion of Life by Frank Thomas and Ollie Johnston - Hyperion