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## 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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# 3. Scaling

Next we need to explore the mathematics of scaling.

## Want to join the conversation?

- I don't understand what he exponent (s) at0:54. could someone please explain it to me?(2 votes)
- When you scale something by two numbers (sx, sy), then you basically just multiply its x-coordinate by sx and its y-coordinate by sy. There isn't an exponent.(8 votes)

- What's the math you use to create a "zoom out" effect. Basically it moves towards the middle of your FOV and gets smaller, but I don't know how to calculate how much to move it towards the middle?(3 votes)
- its also scaling because mathematical scaling also implies translation(2 votes)

- "Don't talk to me or my son again"0:28(5 votes)
- khan academy yay(3 votes)
- Wow it requires two weeks to make a shot?(1 vote)
- I like how u put toy story in it(1 vote)
- add me on snap asapdaddy6964(1 vote)
- What
*would*happen if S was negative? Would the image be flipped either horizontally or vertically depending on the x and y coordinates?(0 votes) - sijdfiosdf sdfnsiudfn sdfiusdnfi sdddnbciu dsifusid fsdufnidsunfsud ds fiu sdfis dfj skjdf sid fisd fiusdfuis dfiu sd(0 votes)
- Can you scale the x and y by the same number at once like variables in programming?(0 votes)

## Video transcript

(techno music) - To hit our design goal given to us from the story department, we'll also have to resize
objects in our scene. For example, I can put Buzz into the shot, but he's clearly not the
size indicated in the sketch. We can change the size of Buzz, say making him twice as big by using
the scaling operation. To scale the object to
twice its initial size, I have to multiply the
coordinates of each point in the object by a factor of two. As before with translation,
I can pick any initial point. Call its coordinates x0 and y0. After scaling it becomes a point x1 y1. This formula shows that the coordinates of each point gets multiplied by two. More generally, making something s times as big means multiplying by s. If s is larger than
one, things get bigger. And if s is less than
one, but still positive, things get smaller. We can summarize this by saying that the mathematics of scaling is multiplication. If the scaling factor in x
is bigger than the one in y, I stretch the object out horizontally. Think about what would happen if the y factor is bigger than x. Also, think about what would
happen if s is negative. We generally need to
both scale and translate objects to put them where we want. I've already scaled the Luxoball so I can position it using translation. Again, as I click on an initial position, you can see where that point goes once it's gone through both operations. The formulas tell us that two operations are being performed. In this next exercise, your assignment is to add to the shot you
created in the last exercise by adding objects that require both translation and scaling operations. Remember if they require rotation, you shouldn't place them
in the shot just yet. (strong drum beat) Take your time, but honestly the animation department has been waiting for this shot for like two weeks. So, see you in 10 minutes.