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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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# 5. Rotation

Rotation turns objects in the scene around. To create a scene, we use all three transformations: scaling (adjusting size), rotation (turning objects), and translation (moving objects). The sequence of these operations is crucial, as changing the order can lead to different results!

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## Video transcript

(springing noises) - So far, we've looked at placement and sizing, which are accomplished using the two operations of translation and scaling. And the animators really need the shot. They're starting to casually scooter by your office and check in on your progress. Assembling a shot generally requires that things be oriented properly as well as being placed and sized. Orienting an object generally consists of one or more rotation operations. So let's go back to our in-progress shot. To position Bo Peep, we'll need all three operations. I'll start by scaling her to her proper size. Next, I'll use rotation to orient her the way the sketch calls for. And finally, I'll position her using translation. We saw earlier that there are simple formulas involving multiplication and addition for the operations of scaling and translation. The formulas for rotation are a little more complicated, involving ideas from trigonometry. Don't worry about the details too much just yet. We'll get to that in a later lesson. For now, I'd like to talk about why I chose to do the operations in the order I did. Scaling, rotation, and then translation. Suppose I started instead with translation, and then rotation, and finally scaling. Bo Peep ends up in the wrong place. So the order can matter a lot. Remember what it's called when the order matters? ^Right. Non-commutativity. Keeping non-commutativity in mind, go ahead and use all three operations to finish your interpretation of Andy's room. Once you're done, you'll get an approval from the director. After that, you can create as many scenes of your own design as you want. Can you make some options that the art department and director didn't even ask for? Making a great film is all about exploring many different options and picking the best one. Have fun!