Math Notes - Episode 1

Vector & Dot products

Based on Freya Tutorial

Hey there. I decided to start a new passion for Maths :’).
Here are some notes taken on a base material offered to us by the great Freya Holmer.

Those personnal notes will follow the video timestamps.

Content

Why Maths ?

So… I decided to focus more myself on math after rewatching the whole Astortion’s Devlog by aarthificial. Recently, he linked a video about Procedural Animations from t3ssel8r which impressed me a lot. I’ve seen this kind of work before, but those guys approch it from an analytical perspective and an elegant equation solving manner.

That was enought to get me started. I’ve already a bunch of ressources on Game Dev Maths which I’ll probably link and store there one day. But for now on, let’s start with freya’s stuff.

1D Vectors (a.k.a Scalar, Floats, Numbers)

We start working with “one dimension vectors” because the same principles apply to higher dimension vectors.

In one dimension, the numbers are treated as float, scalar or single value.

This is a number line : number line image

  • It lies in one dimensional space
  • It help visualize integers and space in between (floating points)
  • Range from [-$\infty$, +$\infty$]

Here numbers can be considered as vectors, distance from origins, steps…

They acts as the representation of something, and within the same context, numbers can be interpreted in multiples ways.

They can be treated in the same manner than higher dimensional vectors:

  • Length (always positive) | Can be called magnitude 
      //x is a one dimension vector
  abs(x) = length # > 0
  • Direction (-1 or 1) | Called sign in one dimension 
      //x is a one dimension vector
  sign(x) = 1, -1 or error
  • Distance (Signed Distance exists aswell !) 
      //a and b are one dimension vectors
  dist(a, b) = |a - b| (or |b - a|)
  dist(a,b) = abs(a - b)
  dist(a,b) = abs(b - a)
  ...
  • Addition (or Substraction) Addition Vizualisation

In this context :

  • Addition is an offset
  • Multiplication is a scale

With this basic knowledge, let’s move one dimension higher ! ___

2D Vectors

Vector normalization

Direction to point

Length

Distance

Point along a direction

Radial Trigger

Dot Product

Assignements ?

Personnal Maths Notes

  • Basics

    Addition to Substraction : $a+b = a + (-b)$

    Multiply to Divide : $^a/_b = a.(^1/_b)$