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- 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.