What does a Bouncing Ball can teach us about animation ?

Two months ago, me and a couple of friends decided to start a little animation group (the Feedbaktor Animus) where we meet together once a week to talk about animation and show us our personal work.

During our first meeting, me and two others decided to start a bouncing ball exercise, as the Animation Mentor student would do it. In the end, it took me one month or so to complete my (actually second) Bouncing Ball. After completing it, I've decided to put together the notes I've take and some things I realized when I was doing  this exercise.

I didn't really know how to divide this in a coherent text since there is a lot of stuff that aren't connected to each other’s. So I finally just happen to divide it into 12 different "Cases Study" I could think off, as I was asking myself this interesting question:

What does a Bouncing Ball can teach us about animation?

*(to be added) Case Study #9 : Weight

Basic Case Study #1 : Timing

Where is our Timing and Spacing within a Bouncing Ball ? Here is a little montage I made with two pages of the Animator's Survival Kit (p.36-37) from Richard Williams.

Here is an interesting quote from Timing for Animation, Second Edition p.2-3.

“Timing [and lets add Posing] gives meaning to movement. […] In nature, things do not just move. You can draw a circle and declare it to be anything from a soap bubble to a cannon ball. We the audience will only understand what it is when we see how it moves and interacts with its environment. […] So in animation the movement itself is of secondary importance; the vital factor is how the action expresses the underlying causes of the movement. With inanimate objects these causes may be natural forces, mainly gravity. With living characters the external forces can cause movement, plus the contractions of muscles but, more importantly, there are the underlying will, mood, instincts and so on of the character who is moving.”

Notice the small fast bounces inside the funnel at 3:00, 

without proper timing, the meaning of this action would not have been convey.

Basic Case Study #2 : Spacing

Here are a few definitions of Spacing :

Myself : From my old notebook !

Timing : The time that something will take to go from one position to the next.
Spacing : The distribution of this time between these two positions.

Kevin Koch : The Missing Animation Principle : Spacing

Timing : Timing is how long something takes to happen [...]

Spacing : It’s the distance something moves from frame to frame [...] spacing refers to the frame by frame displacement of the moving elements. If the element is accelerating, the spacing increases from frame to frame. If it’s decelerating, the spacing decreases. Everything that is moving is either accelerating or decelerating, period.

Jason Ryan : Ramp Up Tutorial , Timing & Spacing pt2

Timing : Is the amount of time or frames that you give to each movements.
Spacing : Is the space or gap that you leave between each frame or pose.

Eric Goldberg : Character Animation Crash Course p. xx & xxii

Timing : The process of determining how long each drawing or position should be on screen on the knowledge that 24 frame equal one second of screen time.

Spacing : The process of determining how far apart the positions should be from one another, based on the knowledge that the farther apart, the faster the action, the closer together, the slower the action.

Keith Lango : Do Me a Favor...

Timing : The time it takes for any object in motion (arm, leg, ball, can of spam, etc.) to go from resting in one position to resting in another new position (pose).

Spacing : How the object in motion covers that distance incrementally from one position to the next. Each new frame shows the object in a new position in two dimensional screen space. The space between where the object was in the previous frame and where it is now in the current frame is the core of spacing. One can manipulate this element to give motion a unique flavor and style as well as the illusion of velocity.

Animation Mentor Webinar on Timing & Spacing : First Part by Aaron Hartline.

Timing : How long it takes something to happen, or to not happen.
Spacing : Frame by Frame displacement of the moving elements within a certain time.


So, as we can see, Spacing is the distance, the displacement, the space or the gap that you leave between each frame or poses. So that at a constant speed of projection, drawing space farther apart (big Spacing) will go faster and drawing space closer (small Spacing) will go slower.

Now here is an interesting case : A Bouncing Ball Spacing VS A Pendulum Spacing

Notice how the Primary Breakdown (blue) actually Favor different Keys (red) in these two example to define the Spacing of the move (and thus where the slow-out/slow-in will happens). Because the acceleration and deceleration doesn't happen at the same time in a Bouncing Ball and Pendulum, the first Breakdown (blue) isn't draw at the same place in each example.

Case Study #3 : Tangent VS Arc

Now this is something I didn't realize until someone explain it to me at work, when I was already way ahead in my Bouncing Ball animation !

Here is the thing. If you want to do a bouncing ball animation with only three keys for each bounce (two for the contacts and one at the top of the arc). You have to realize that when you want to adjust your spacing by pulling-out the tangents so that you have a fast-slow-fast motion, you are also changing the Arc of the bounce, something you may not necessarily want.

The solution for that particular Bouncing Ball case ? Just do it the "good old way" and define your motion with drawings and not with tangents, so that you can adjust your Spacing without changing your Arcs.

Case Study #4 : To be or not to be Alive

When we start animating a bouncing ball, one of the question we can ask ourself is : Do we want our ball to look like it is alive or not ? What is the "underlying causes of the movement"  (see Timing for Animation quote above) ? Does the movement of the ball is only driven by "natural forces, mainly gravity", or does it seem to have some "underlying will, mood [and] instincts" ? Or maybe it could be the combination of the two; being alive in some parts and not in others.

What are the underlying causes of the movement?

Case Study #5 : Why to not define your acceleration & deceleration (slow-out & slow-in) with your timing in 3D :

Here’s a little something I realized when I was doing some rope animations at work. As I was working on this pendulum type of motion, I once did a mistake. I had all the poses of my character spaced evenly on screen. So that to define my slows-in and slow-out that is happening at each end of the swing, I had actually moved the keyframes over my timeline to define my spacing, with my timing. In other words, I had no spacing On Screen, between my Poses, but by moving my keyframes around I had still manage to define my Spacing between each frames, by playing with my “timing” (the time between each even poses I had).

As I’m explaining below, even if this can work in 3D to a certain extent because of the free in-betweens, arc and slow-out/in that we get with spline interpolation, it is just not a good way to define the spacing of an animation. Here’s why: 

(1) Spacing wise it’s even, but timing wise it’s not. It is an odd way to do it, but we can manage to get our slow-in, slow-out (Spacing) between each frame by playing with our timing.
(2) Timing wise it’s even, but Spacing wise it’s not. Good


(1) It’s working because of the spline interpolation, which is giving us free in-betweens, arc and slow-in/out. As my poses are spaced evenly, it would not have work if I didn’t add in-betweens (more frames) between my poses.
(1) In stepped “2D” mode, there will be no fluidity when it’s slower because there’s not more drawing close together as it slows down.
(1) You loose control over the exact spacing you would want.
(1) Since there is no spacing on screen, you can not check it by “flipping” your timeline keyframes (poses) forward and back (unless you go frame-by-frame).
(1) Odd, the keyframes in the timeline would be positioned the exact same opposite as a spacing chart would be.

Overall, it’s not that you can’t define your spacing with your timing in 3D, but more that doing this doesn’t make that much sense !

Case Study #6 : Anticipations

Here are a few definitions of Anticipation! Don’t hesitate to take a look at the reference since these are just sentences without explanation or examples:

“An Anticipation is a sub-poses or a minor pose of varying degree of intensity […], that announce something is going to happen” 
-Keith Lango, VTS 06, 12:00

“Anticipation allows the audience to forsee what the character will do next. A pitcher rearing back would be the anticipation before the pitch
[…]
So again anticipation, always go the opposite way of the main action. So the character is going screen left to screen right, screen bottom to screen top : Go ahead and do an anticipation in the opposite direction. “
–Jason Ryan, Ramp Up Tutorial , Anticipation

“So, Anticipation is the preparation for an action. Anticipation takes place in almost every action – and certainly every Big action
[…]
The rule is : “Before we go one way – First go the other way”
–Richard Williams, The Animator's Survival Kit p.274 - 275

Let’s look at a first example of an anticipation with a bouncing ball. Notice how the Bouncing Ball of Krzysztof Boyoko is doing a little anticipation going up before the main anticipation going down with his ball. It is what Keith Lango or Jason Ryan would call a “Micro-Anticipation” [Keith Lango VTS 08, 25:40] or a “Secondary Anticipation” [Jason Ryan Ramp Up tutorials; Anticipation 5:15]. These little anticipation  that are happening before the main one will be feel more than seen by the audience. As they are preparing the audience for the main anticipation, which is almost like an action itself.

As a second example done by Daniel Huertas, here is a very broad anticipation followed by a super-fast action showcasing how anticipations and the timing and the size of an action are related. As you can see in the table below base on Keith Lango VTS [VTS 06, 11:10], if you have a very fast action, it generally means that you will have a long (big) anticipation as there is an inverse relationship between the timing of the action and the magnitude of (the energy store during) the anticipation needed to sell that action.

“A lot of thing about anticipation is about energy. To make things move you need energy, and to make things moves fast or far you need more energy. And so what anticipations are is the building up of energy to make things moves.  […] If you only build-up a little bit of energy you are creating then the expectation of a small movement.   If you create a large build-up of energy then you are creating in the audience the expectation (or the anticipation) of a large movement. “ -Keith Lango, VTS 06, 18:15

Case Study #7 : Physique

Here are a few interesting points to remember about the physic of a bouncing ball. I extract those from the resources below, which I recommend you to read since there is interesting stuff in there.

Interesting Points:

• All ballistic objects move on parabolas.

• Gravity is an accelerating force. A ball that falls from 2 feet doesn't take twice as long as a ball that falls from 1 foot.

• In a parabolic arc the horizontal spacing is constant and uniform while the vertical spacing is not, due to gravity.

• The faster the horizontal speed, the flatter the arc, and vice-versa. 

Ressources :

Here are two scan of the book Animation the Mechanics of Motion by Chris Webster. I would not especially recommend his book since the animations on the DVD kind of "suck" a little bit. I always found it bizarre when someone releases a book (or online tutorial) supposed to teach you something about animation but the animated examples don’t look very good…

Animation the Mechanics of Motion p.21

Animation the Mechanics of Motion p.20

Here is a discussion that surface on the 11 Second Club forums recently about Bouncing Balls. There are some interesting interrogations in there, as this one about the timing of successive bounces. Because the obvious isn't as obvious as we could think:

Timing is reduce after each successive bounces

The best physic papers on Bouncing Ball you can find around are probably the ones from Alejandro Garcia. The work he did on these is really amazing, everything is explain with lots of concise but clear text and interesting visual examples.

-Physics of Patch of Action
-Physic of Timing and Spacing

For instance:

Case Study #8 : Variation in Timing and Action

When a Bouncing Ball is bouncing around (being alive or not) in some sort of setting (as an obstacle course), there should be some variation in the Timing and Action of the ball, or it will be uninteresting and boring to watch. Having this variation mean there should be some slow bounce and fast bounce (Timing) and some little bounce and big bounce (Action). In addition to the bounces there could be some sliding or rolling, some little anticipation and big anticipation and maybe some slow movement with high frequency movement on top of it. At the end of the day, the idea is to get contrast in there, some variation.

Victor Navone and Aaron Hartline are talking about this in the really interesting Webinar on Timing & Spacing they did with for Animation Mentor. Also, on the exact same topic, take a look at this post on the rule of thumb of 3-Speeds and this post on Rhythm & Texture from Victor Navone own blog.

Case Study #10 : Getting Movement Within the Movement

Getting movement within the movement, getting action within the general action. This is kind of a rule of thumb I'm sometime using when things are not as interesting as they could and I'm wondering why. I had taken the general idea from Richard Williams's book (see pages 213, 222 and 224), but beside the examples he is showing, it could be apply to all sort of situation.

The basic idea is that instead of having a cube (for instance) going from one position to the next in a strait linear line, adding some acceleration or deceleration, some arc, some angle change will give movement within the movement. A video game character jumping from the fifth floor of a building with his arm and legs rotating  around may be more interesting that if his arms where just moving over his head gradually (although it will depend of what you want) because we get movement within the movement, or action within the general action. The transition animation of a character holding a ledge and climbing up going to his run cycle will be more interesting if the body is going slightly to the side and tilting a bit to get some angle change instead of going up in a straight line, even if the speed is not linear.

"I call this 'putting the juice in' " -Mike Brown

See how the fourth ball has a slight arc to the side, adding the "juice", the movement within the movement to this Bouncing Ball.

Case Study #11 : Squash & Stretch

Here are list the three squash & stretch ideas that a Bouncing ball highlight in animation.

1. As with the Timing of bounces, the amount of Squash and Stretch depend of the material nature of the Bouncing Ball. For instance, rubber is flexible and therefore is subject to shape changes. If the ball was a metal cannonball, it would not be subject to shape change (squash & stretch) and this gives the animator the tool to define the nature of the ball's material.  

2. As a general rule you should ensure that the volume of the object you are animating is not changed; it should neither gain or lose mass. While the shape of the characters and objects may change, they may be flattened or extended; they should not lose or gain volume.

3. When does it squash, and when does it stretch ? When a flexible rubber ball hits the solid ground, it will distort in shape. In other words, it will "squash". The higher the bounce and thus the faster the speeds of the ball, the more squash there will be when it hit the hard ground (1).

Note however, that at it's apex (upper) positions the ball do not squash, as it is not subject to any contact with a hard surface like the ground or is even being distorted by velocity. Thus, because it's coming to a halt at the top of the arc, the ball returns to its natural, circular shape (2).

But this is not true however, on the way up and on the way down. Where the ball will be stretch as it is being distort by the speed it is travelling. As the ball is going less higher and faster, the amount of distortion (stretch) will then be reduce within each successive bounce (3).

Case Study #12 : Thinking as a Bouncing Ball, Thinking High Level

An interesting motion doesn’t come from separate body parts. It doesn’t come from the movement of an eyebrow or from the movement of separate limbs. Nope, an interesting motion come from the contrast of the movement that originate from the abstracted mass of the body.

So the important movement isn’t the one that generate from separate body parts, but from the mass of the body as a whole. This is where a bouncing ball can comes handy. By imagining your character as a bouncing ball you can think more high level. You can think of your motion not in terms of limbs, but in terms of a ball, a cube, or multiples balls moving around while trying to convey an action or performance.

Here are a few examples:

A montage I did. The Vertical Jump from God of War 3 can be breakdown as a Bouncing Ball

From Preston Blair. The bottom character acts as a Bouncing Ball

See also the Brendan Body's lecture on Bouncing Ball and walks, interesting stuff.

"Let's now see how the bouncing ball applies to an animated character [walking]"

A walk with balls !

And finally, don't forget to check the Animation Mentor Webinar : Give Meaning to Movement: Timing and Spacing in Animation Explained where Aaron Hartline is presenting a lot of Bouncing Ball "high level thinking" example during the first two part of the Webinar.

That's a pretty ad

Hope that wasn't to long. No wait, It was !


Francis.