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This video introduces the transformations we'll be using in the rest of this lesson.

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Disney Pixar
07/14/2021
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First let's think about how to rotate some really simple points such as (0,0) and (1,0)

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First we'll use the slope intercept form of a line to define each frame along a straight line.

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First we need to make sure we understand exactly what happens in the split & average steps.

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07/14/2021
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Find out how we can make curved lines using straight ones using the string art construction.

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07/14/2021
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What happens if the director changes their mind and asks for two headed robots?

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First we'll review weighted averages of two points and extend the idea to three points. Practice weighted averages of two points in Environment Modeling if you haven't seen it before.

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How can we calculate a weighted average between two points? (pssst. This video is super important).

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07/14/2021
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Next lets build a diagram that break rotation into smaller parts. The next exercise will give us a chance to build our understanding of this diagram.

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07/14/2021
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Let's look more closely at how light behaves when it strikes an object. We'll cover diffuse and specular surface responses.

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07/14/2021
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First we'll review De Casteljau's algorithm using three points. Then it's your turn to figure out how to do it with 4 points!

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07/14/2021
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Let's review the multiplication principle which allows us to quickly count the number of possible robots.

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Now we can combine split and average into a single operation called subdivide.

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Next let's extend the averaging step from the previous lesson to include multiple points. Now we'll need to calculate positions using a weighted average.

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Where does the string touch the parabola? See if you can come up with your hypothesis!

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Now we are ready to calculate an intersection point using our ray CP (parametric form) and our line AB (slope-intercept form).

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Now that we have a feeling for constructing permutations let's introduce the factorial formula to make counting them easy.

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07/14/2021
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In this video we'll uncover the connection between the previous diagram and the rotation formulas. Repeat viewing suggested!

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07/14/2021
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We can use de Casteljau's algorithm to calculate curves using any number of points.

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07/14/2021
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Let's take a closer look at the weights used during subdivision. Do we have to be careful when selecting weights?

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07/14/2021
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Let's look more closely at how light bounces when it strikes an object. We'll cover reflected and refracted rays.

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07/14/2021
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Are we really creating parabolic curves using this construction? Let's gain some insight first.

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Use an array to store many objects as well as create any shape you can imagine. Click here to review objects.

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