Arc
From Anipedia
Contents |
[edit] Introduction to Arcs
You see a leaf blow through the wind, a human walking, or a worker hammering in that last nail. If you take a moment you can see that all of these things use arcs while in motion, in fact almost everything in nature uses at least one! Let's consider what arcs are, how arcs are used, and how they can help you with animation.
[edit] What are Arcs?
An arc, in mathematics, is a part of a continuous curve around a point. So, if a point does not move, and the object does not follow a part or whole of a circle path, then we know it is not an arc. Take a look at figure A, 1 is an arch, however figure 2 is not since the path is not a circular path but a compound curve.
Arcs must follow the point they are connected to. In figure B there are 10 frames of animation. At frame 7 the point jumps to the right; notice how the arc responds.
From this, we see that arcs follow the point without delay.
Note: A compound curve and an Arc are very different. An arc can only contain a single continuous curve, a circle. However, compound curves can contain very intricate designs.
[edit] Arcs in the Real World
Arcs are common place in the real world, take an example with Figure C. Does C-1 or C-2 look life like? Of course C-2 is the obvious choice, as the pendulum has followed a natural path that kept it's length!
When we move, we use arcs, our wrist moves in an arch around the elbow (Fig C-1), are fingers use arcs (Fig C-2), and many other parts of the body. This concept also holds true for animals and machines.
[edit] Using Arcs in Animation
We have determined what arcs are, how we use arcs in the real world. But what about when animating? Arcs are used whenever we need to keep something consistent in length. Without them, our animation will not feel life like and confuse the average viewer. This does not mean we should use arcs for everything. If you have a non rigid object, such as cloth, string, or hair; use the arc as a guideline, but add appropriate follow through(Fig E-1). If an object is hit, make your object follow the new arch if it had less inertia than the object hitting it, and vice versa.(Fig E-2).
(Figure E currently being redrawn)
Arcs can also be used to help you do better 3D effects, by drawing an arc, we get a guide on how it should be done. In figure F-2, we see a top down view of the arc, and in figure F-1, the animation I produced with it's assistance.
[edit] Conclusion
We now understand how arcs work and how they can help you animate better. For further study, try remaking the tutorial animations for better comprehension.
