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### Course: Pixar in a Box>Unit 11

Lesson 2: Calculating parabolas

# Weighted average of two points

How can we calculate a weighted average between two points? (pssst. This video is super important).

## Want to join the conversation?

• What exactly is "t"? And if it is possible to find the arbitrary constant "t"; how do I find "t"?
• You can think of t as the percentage of the way a point is from A to B. So:
When t = 0 the point is 0% of the way to B, so is equal to A.
When t = 1 the point is 100% of the way to B, so is equal to B.
When t = 0.5 the point is 50% of the way to B, so at the midpoint from A to B.
When t = 0.25 the point is 25% of the way to B, and so on.

t can be any number from 0 to 1. If you know the position of A and B and P, then you can calculate t.

If P = A(1- t) + tB, then you can just look at the x-coordinate of each point with the equation:
Px = Ax(1 - t) + tBx
Px = Ax - tAx + tBx
Px = Ax + t(Bx - Ax)
Px - Ax = t(Bx - Ax)
t = (Px - Ax) / (Bx - Ax)
That will work so long as Bx is not equal to Ax. If it is, then use the y-coordinates instead.
• what do you mean by 'B is weighted twice as heavily as A'?
• The word Weight is a measure of force pushing or pulling on an object due to gravity. This means that during the calculation, when we consider B to measure two times the value of A, we are saying that B has two times the gravitational pull of A. This is the same as saying B weighs twice the value of A. From we hear Tony explain that the force of weight from B is pulling M two thirds (2/3) of the segment length, and is twice the force of weight at A, which only pulls back one third (1/3). The base of 3 is used for taking the average because we have 1A + 2B, or A + B + B.
• I need some BIG help by now. I am in 4th grade and I recently found out that linear interpolation and blah blah blah is 8th grade math. So, if you can help me, please reply-post an linear interpolation problem and then simplify it so your a fraction of 1 percent more than average 4th grader can understand. PLEASE!! IT WOULD HELP ME A LOT!!
( confused emote )
• are there any other videos to help me understand the conceps of the algebra in this video?
• Yes, KA's math section has practically every concept a math student could ever want to learn. A basic understanding of algebra is needed to fully understand these videos, so you might want to try the Algebra 1 section or Pre-Algebra section to find out what you need to know.
• how do the workers come up with the ideas to make the objects and characters? Also how do you create the items that you want to use in these disney shows
• It's outside the scope of this lesson, but I'll answer anyway.
When someone has an idea to make an animated film, the first thing they start with is story. Maybe one person writes the entire story and presents it, or maybe lots of people talk about it and throw ideas around. However it happens, eventually they have an outline of the kind of story they want to tell, and they have some idea of the kinds of characters and environments they'll need to tell it.

These writers, producers, and creative directors (the development team) describe the characters and setting to concept artists. The concept artists start by making lots of rough sketches of the characters, showing them in batches to the development team and getting feedback on what works and what doesn't. Then the concept artists return to making drawings. This time they're more detailed, and they incorporate the feedback they got. The new drawings are shown, and this process continues until each character and the setting satisfy everyone involved. The concept artists may also make sculptures of characters, called maquettes, so that everyone can be sure that the character works as well in three dimensions as it does in two.

From there, the process is pretty much as described in the Pipeline Video at the beginning of the course: https://www.khanacademy.org/partner-content/pixar/start/introduction/v/pipeline-video
I haven't watched them yet, but I would imagine there is a lot more detail on the actual process of modeling characters in the Character Modeling lessons: https://www.khanacademy.org/partner-content/pixar/modeling-character
• thanks bro