This video introduces the transformations we'll be using in the rest of this lesson.
How do we keep track of how many robots we've made?
Before building characters you need to define individual shapes using objects.
Now we attach our particle to a spring.
First let's think about how to rotate some really simple points such as (0,0) and (1,0)
First we'll use the slope intercept form of a line to define each frame along a straight line.
First let's look at ray tracing in 2D using a simple example.
First you'll connect shapes together using joints that rotate.
First we need to make sure we understand exactly what happens in the split & average steps.
Let's start by drawing every frame, one by one...
Find out how we can make curved lines using straight ones using the string art construction.
What happens if the director changes their mind and asks for two headed robots?
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.
How can we calculate a weighted average between two points? (pssst. This video is super important).
Introduction to the basics of ray tracing.
Now we add a horizontal component to our system.
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.
Let's look more closely at how light behaves when it strikes an object. We'll cover diffuse and specular surface responses.
Connecting key poses with straight lines is called linear interpolation.
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!
Introduction to syntax for shape objects
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.