Explore how midpoints are used to describe the "string art construction.".
This video introduces the parametric form of a ray in 2D.
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!
Let's review the multiplication principle which allows us to quickly count the number of possible robots.
Let's build some snakes to get us thinking about permutations.
Now we can combine split and average into a single operation called subdivide.
Now we can begin laying out our scene! Starting with translation...
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.