Math meets artistry

- Hi, I'm Rob Jensen, and I'm an animator. Before we talk about computer animation and algorithms and all that, let's just talk about what animation is at it's core. All animation is based on the same idea. Making changes to a series of images and playing those images back in sequence. Now in hand-drawn animation, we do this by drawing. Animators draw key poses and then draw a series of pictures we call in-betweens that connect the motion from one pose to another. It's a lot of drawing. In computer animation, we animate by moving virtual digital models. We call this posing. The poses we create are translated into coordinates that are recorded on a spreadsheet. The computer fills in the in-between images. These in-betweens are the result of a computer interpreting what motion would move an image from this pose to that pose. Of course, the computer can't act, so it gives us this. We refine the in-betweens to turn this robotic motion into a polished performance like this. And there are many different ways of filling in the in-betweens. But each can be described using a mathematical function called a spline. And this is where the math meets the artistry. The simplest way to see this spline idea is through a bouncing ball. I'm going to make it bounce from here to here with four main poses that I define by setting keyframes. The computer draws all the other frames by evaluating the spline. By default, the computer makes a linear interpolation of the motion and we get something that moves at a constant speed. Hmm. Now from physics we know that the ball should accelerate on the way down and decelerate on the way up. I can adjust the shape of the spline to change the timing. Now we got something that looks more realistic, but it's still pretty generic. As an animator, it's my job to bring to life a specific character. So I need to ask myself some questions. Is the ball heavy and depressed like this? Or maybe it's happy. Maybe it's a balloon. Once I answer these questions, I can choose what kind of spline I think will have that effect in the motion. And this gets even more exciting when you're looking at a character and their physics because how a character moves says a lot about who they are. For example, Mr. Incredible in this scene, the animation needs to show him lifting up a train car. Now, in animation, you can make that seem really quick and easy, but the director didn't want that. He wanted the audience to know that Mr. Incredible could do amazing things but that it took a lot of effort to do them. So, the way we define the speed of the in-betweens will make the difference between the train looking light or the train looking heavy. So, let's be clear. The computer helps us a lot, but ultimately this job is really about acting. But instead of being in front of a camera, you're taking the performance and breaking it down into tiny little 24th of a second increments, and expressing those in an abstract mathematical function. Pretty cool, right?