Now you'll need to start moving your lamp around using translations.
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.
Where does the string touch the parabola? See if you can come up with your hypothesis!
Using Bezier curves we can get smooth motion between keyframes.
Now we are ready to calculate an intersection point using our ray CP (parametric form) and our line AB (slope-intercept form).
Now that we have a feeling for constructing permutations let's introduce the factorial formula to make counting them easy.
In this video we'll uncover the connection between the previous diagram and the rotation formulas. Repeat viewing suggested!
Let's apply what we just learned to calculate the touching point.
We can use de Casteljau's algorithm to calculate curves using any number of points.
Let's take a closer look at the weights used during subdivision. Do we have to be careful when selecting weights?
Let's look more closely at how light bounces when it strikes an object. We'll cover reflected and refracted rays.
Are we really creating parabolic curves using this construction? Let's gain some insight first.
Use an array to store many objects as well as create any shape you can imagine. Click here to review objects.
Now you can start scaling your shapes to make your lamp look younger.
Next we need to explore the mathematics of scaling.
Now you are ready to start subdividing your own shapes with more than 4 points!
How can trees be combined to count robots with many parts?
401(k)s (and how they compare to IRAs). Created by Sal Khan.
Now it's time for a really meaty problem! How can we count the number of possible casts when given a large set of robots to choose from?
We need to be careful with the order of scaling and translation. But why?