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## Geometric transformations

# 2. Translation

## Video transcript

(bouncing noises) - Now that we know how to plot points on a coordinate plane, we're ready to start designing a shot. Let's take a closer look at this sketch that we got of Andy's room from Toy Story. We can see that Buzz and Bo Peep are laid out on the floor and on the bed in sort of a haphazard sort of way. We can also see in this sketch, that there's a question. Where do we want to put the lamp? Do we want it next to the bed, so that the person who lives here can use it? Or do we want it on the dresser, to mean that the adult is using it? Everywhere you put something, means something. And really good computer graphics tells a story in every single placement of every single prop. To build the shot, we've received this set of objects from the modeling department to work with. At Pixar, we call such a collection a model catalog. Since in this lesson we're working in 2D, our objects are 2D images. But when we do this for real in a Pixar movie, our assets are 3-dimensional models. In either the 2D or 3D case, we pick a reference point on the object to aid with placement. We could choose any reference point we like. In this lesson, we'll choose the lower left corner. Objects brought into the shot from the model catalog will appear with the reference point at the origin. To lay out my shot, I start with the dresser, since it's one of the bigger forms I'll need to work with. Once the object is in the shot, I can position it wherever I want using the translation operation. For instance, lets move it five units to the right, and five units upwards. To translate the entire object, we have to translate each point in the object. So, if I pick this point on the initial object. Call its coordinates x zero and y zero, it gets moved to this point after translation. Call the coordinates of this translated point x one and y one. This formula over here tells us that the mathematics of translation is addition. As I click on a point in its initial position, you see where that point goes as well as what's happening to the coordinates. So whenever you see objects changing position in our films, you know that translation, and therefore addition, is going on under the hood. Your first assignment is to select objects from the model catalog to create a first pass at that drawing you got from the story department. To keep things simple for this first assignment, we've only given you the translation operation, so you won't be able to layout the whole shot. Your job is to figure out which objects you can place using only translation. You shouldn't pick objects that are going to require re-sizing or rotation just yet. And if you add an object by mistake, you can always click remove. Good luck.