So, we've learned how to do rotations today and we're using tracing paper. So, we have a coordinate grid with our shape here and we want to rotate it 90 degrees counterclockwise about the origin. So, that means we're rotating it around at this point here. The origin is the point zero where it would the x and y axes intersect. So, we learned how to rotate it using tracing paper and I'm going to use an example with a transparency. So, it'll be easier for you to see on the video but, what you're going to do is use your tracing paper draw the axes and the shape on the tracing paper. And since we're rotating it about the origin, you're going to put your pencil point right on the origin and you're going to rotate it or, spin or, turn the tracing paper around. Now we are moving it counterclockwise, which means we are rotating this way all right, and, we're rotating 90 degrees so that means when the x-axis hits the y-axis we've rotated it enough. So, rotate it. Boom. There it is, 90 degrees. And there is our rotated shape. I'll do it one more time for you so here's the original. Put my pencil in the origin because that's where we're rotating it around and counterclockwise until the axes line up again. BAM. There it is right there and there's our new shape.

At Pixar we build our movies shot-by-shot. A shot is something we make by staging our characters in a set and then framing them up through a camera. Every time the cameras point-of-view changes...That's a new shot. On average, a Pixar movie is made of about 1,800 shots.

That's a new shot almost every three seconds. In animation we don't just dive in and start creating shots. First we need to figure out the story. And we do this by making a story reel. It's a fast, rough version of the film made of tens of thousands of drawings. The story reel does more than just tell the story. It hints at a lot of things, such as composition, camera movement, performance and location. The story reel gives us a good place to start thinking about how we're gonna make these shots for real. Real, like in the virtual, three-dimensional world of computer graphics. And math is literally the foundation for all the processes we use to create these films in the computer. This lesson will show you how geometric transformations, which are basic functions to manipulate the position, orientation, and size of an object, are an essential part of building our shots. You ready? Of course. Let's go. I work in the Set's Department as a Set Dresser. Often, the set starts as just an empty room. Using the story reel, and reference from the art department, I will work out what objects we need to include in the set initially. At this stage, before cameras are in there, it's not about making the set pretty. It's about supporting the action. So I only include things that are essential in staging the shot. I select the virtual models I need, and they appear in the center of the set. I move them into place around the room, turning them and re-sizing them if necessary. Each of these changes to the model is accomplished using geometric transformations. When I'm done with this first pass I send it to staging. My department, Camera and Staging, is where we figure out how to shoot the movie through the lens of a virtual camera. So let's take a look at the shot we're gonna make. Oh no! Our dinosaur has escaped. In film-making, camera movement is a powerful tool to convey emotion in your audience in a subconscious way. Is the camera hand-held? On a dolly or a crane? Is the character experiencing some important moment? A moment of significance that we're pushing in on?

For this shot we're gonna follow the action with our camera, panning with Bonnie as she moves through the space. Oh no! Our dinosaur has escaped. When we're done setting up the camera, the shot goes back to Set Dressing. Now that I know what the set looks like through the camera, I can take a more detailed pass. I'll add objects to make the set feel more believable and support the story. Sometimes this means adding a lot of stuff in messy piles to feel like a teenagers room. Or fill the crates in a bookshelf so it looks like a daycare but feels like a prison. And all that math? Well, we use geometric transformations at every step of building the shot. In this lesson, you'll get a chance to use geometric transformations, and explore concepts as simple as addition and as spicy as trigonometry to build your own shot.