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### Course: Pixar in a Box > Unit 14

Lesson 1: Geometric transformations- Start here!
- Introduction to geometric transformations
- 1. Coordinate plane
- Graph points
- 2. Translation
- Laying out a scene using translation
- 3. Scaling
- Scaling items in a scene
- 4. Commutativity
- Commutative and non-commutative transformations
- 5. Rotation
- Finish your scene!
- 6. Composite transformations
- Composite transformations
- Getting to know Fran Kalal

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# 1. Coordinate plane

Learn how Pixar uses geometric transformations to create movie scenes. Starting with large forms like walls and floors, animators add elements like furniture. These items are positioned, sized, and oriented using translation, scaling, and rotation operations.

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- Oh my goodness, I would love that job! I love making sets, and virtual sets are even better! What would you suggest I study, in order to, say, get a job doing that at Pixar?(10 votes)
- At1:13, what does z stand for? I know that x is how far left or right it is and y is how up or down it is. But when I heard the letter z, I was really confused.(8 votes)
- You can initially say that Z stands for Zoom In and Zoom Out but it is used to move objects in forward and backward direction so that you can view them more near to camera.(6 votes)

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- Presto is the proprietary software developed and used in-house by Pixar Animation Studios in the animation of its features and short films.(2 votes)

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## Video transcript

- Hi, I'm Fran, a technical director here at Pixar Animation Studios. I'm talking to you today from the lobby of one of the beautiful buildings of the Pixar campus. As we learned in the previous video, when we create shots to make up our movies we need to assemble the environment where the story takes place. If I were to build this kind of environment, I'd start by placing the really big forms like the walls and the floor. Then I'd place the dramatic elements like this gargantuan fireplace behind me. Then I'd move down to the medium sized elements and do selection and placement of the couches, tables and chairs. Finally, I'd move down to the really small details like the magazines on the table and the pieces of wood in the fireplace. All of these items need to be positioned using the mathematical operation of translation, properly sized using the scaling operation and oriented using rotations. These operations are all examples of fundamental geometric transformations. We'll spend the remainder of this lesson looking more closely at them. For our films, these transformations control what's going on in a virtual three-dimensional space. ^Meaning that each point has three coordinates, ^X, Y and Z. ^But for this lesson we're gonna simplify a bit and look at laying out floor plans in two dimensions, like we're viewing them from above. ^So points need only two coordinates, X and Y. ^The X coordinate says how far to the right a point is, ^and the Y coordinate says how far up it is. ^This point for instance has X coordinate three ^and Y coordinate five. ^Before we begin building our own shot from Toy Story, ^let's review how to plot points in 2D using the next exercise.