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How do animators use math?

The animation community is comprised of people who need to know a lot of math to create the motion of their characters. They can’t be too excited about math, so let’s get something straight: maths is not the reason why animators animate. It is very much about finding the right equation that will produce the motion you need.

For example: an equation to generate a specific length of length is the equation (length + time): (length * time) = length. An animation that is meant to be in perspective is simply a list of angles: length is a list of angles. For example:

animated in 3D:

height = 0 height = 2 height = 3 height = 4 width = 0 width = 2 width = 3 width = 4

animated in perspective:

height = 0 height = 2 width = 0 width = 2 width = 3 width = 4

So here is an equation to generate a length of 3: length * (2 + 0.2 * 1) = 11.3. The same thing can be found as distance + time (with the addition of 0.2 to the end as well), but it is not the equation that leads animators to generate different movements. Some animators work with a 3-step equation and another that uses just the first step (for example the 2-step equation):

animated in 3D:

height = height + height2 * (1) height = 2 height = 3 height2 += height3 height = 11.3

animated in perspective:

height = height + height2 width = height2 + height width = 4 width = height2 + height3 width = 11.3

So what is math? Let’s start there. There is one mathematical thing that is absolutely essential to all animation: a constant called a constant! You can’t just add variables and call it good. A constant is something that keeps the animation constant. Some animations call it a formula.

This is because constant math is something that’s created by making the variables bigger, not smaller. It is the constant that defines the equation. For example:

height = 0 height = 2 height = 2 height = 3 height = 4 height2 += (height * height) * height height = 3

animated in 3D:

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height = 0 height = 2 height = 2 height = 3 height = 4 width = 0 width = 2 width = 2 width = 3