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### Course: 8th grade (Eureka Math/EngageNY) > Unit 2

Lesson 1: Topic A: Definitions and properties of the basic rigid motions- Introduction to geometric transformations
- Identifying transformations
- Identify transformations
- Translations intro
- Translating points
- Translate points
- Translating shapes
- Translating shapes
- Translate shapes
- Determining translations
- Determine translations
- Rotations intro
- Rotating points
- Rotate points (basic)
- Determining rotations
- Determine rotations (basic)
- Reflecting points
- Reflect points
- Reflecting shapes
- Reflecting shapes
- Reflect shapes
- Determining reflections
- Determine reflections
- Translations review
- Rotations review
- Reflections review

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# Introduction to geometric transformations

How are virtual sets built in the computer? Pixar uses geometric transformations in animation to manipulate the position, orientation, and size of objects. This process involves story reels, set dressing, and camera staging. Each shot is carefully crafted, using math as the foundation!

## Want to join the conversation?

- How much does RenderMan cost?(4 votes)
- https://renderman.pixar.com/store shows different pricing options(2 votes)

- how do they do animations with computers instead of paper?(2 votes)
- It's much like animation on paper, or flipbooks, in that you use frames shown together really fast to assume motion. But computers make it easier, so you only have to put the start of the movement, and the end of the movement, and the computer calculates what should be inbetween.(4 votes)

- i want to know how do they decide what to put in the scene or how they will make it realistic enough(2 votes)
- That is left to the Art and Design departments.(2 votes)

- what are geometric transformations(2 votes)
- To be exact, how many years does it take to make a movie?(2 votes)
- At3:03theres a white dot and beep again!(2 votes)
- Isn't it easier to take a video or something. Why do we need graphics and stuff like that(3 votes)
- I agre cartoons are a ton of frames put together by graphics. there are about 24 frames per second in toy story.(0 votes)

- How long does it take to make the art work of the story?1:17(2 votes)
- how do the animations work?(1 vote)
- How do you use Math in transformation?(1 vote)

## Video transcript

- 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'a 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.