Maths basics

In this chapter, we'll regard numbers as 1D vectors. This way, we can reuse the knowledge to abstract things to the second and third dimension.

(TODO: add a nice scale diagram with examples here)

The length of a number:

abs(x)

Lengths are always positive, so the length of a number is the absolute value of the number.

• the number 1 has a length of 1.
• the number -2 has a length of 2.

The direction of a number:

sign(x)

There are two directions when moving on a number scale. Left (-1) and right (1). The formular for getting the direction of the number is x / abs(x). In the world of vectors, this would be called "normalized" vector.

• the direction of the number 5 is 1
• the direction of the number -2 is -1
• the direction of 0 is not defined

The distance between two numbers:

abs(b - a)

The distance between two numbers can be calculated by subtracting the numbers and measuring the length between the two.

• The distance between -1 and 1 is 2

Interpolation between numbers

Linear Interpolation

Linear interpolation is used to transition between 2 values.

The function for interpolating between 2 values looks like this, taking 2 values a and b and a third parameter x = [0..1].

mix(a, b, x) = a * x + b * (1 - x)