Tree diagrams allow us to visualize these counting problems using any number of parts.
Next you'll use functions to *store* your deformer functions.
Okay we know how to calculate the touching point, great! Next let's think about how we can prove this is true.
Next let's build a blade of grass using a parabolic arc as a spine.
Created by Brit Cruise.
Case study from Monsters University.
Let's breathe some life into our ball using a key animation principle: squash and stretch.
Now let's think about how subdivision would work in 3D.
Next we need to throw away the slope-intercept form and use the line equation instead.
Bonus! In this video we'll connect the degree of these curves to the number of control points in the construction.
Now we are ready to ray trace in 3D. We'll look at the problem of ray triangle intersection.
Finally, let's bring our parabolic arc to life!
Now it's your turn to drive. In this video we'll present you with a casting challenge to complete using everything we've learned so far.
Review of how to write a function (starting with translation)
Why do we divide the number of combinations by the number of permutations?
Try out your deformers on a face.
Finally we'll need to rotate object to finish our scene.
Now we just need to determine whether our intersection point is inside or outside the triangle.
Let's put everything together. Get ready for a really powerful formula: the binomial coefficient (warning: you may need to watch this a few times!).
Time to get a little mathy. Let's look at the general form for any transformation.