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?
Mrs. Rowhani's third graders learn about matter and energy by building a Spout bot with Khan Academy. Special thanks to: Santa Rita's volunteer parents, Kami Thordarson, Karen Wilson and of course Laleh Rowhani the class teacher. Created by Karl Wendt.
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?
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.