Math

I hate it. Always.

One does not need to be good at Mathematics to learn game development. It helps to know some things but you learn it when you need it. The basic things that is used the most is trigonometry and linear algebra with vector and matrix operations.

Arithmetic

Algebra

Linear algebra

Geometry

Coordinate Systems

Geometry

Surfaces

Analysis

Curves

Function

Applied

Statistics

  • Scalar variables will use lowercase letters in italics: a, b, x, y.
  • Vector variables of any dimension will use lowercase bold letters. a,b,u,v.
  • Matrix variables will use uppercase letters in bold: A,B,M,R.
  • Angles are given by lowercase Greek letters. α, β, θ, λ.

Reference

Fast, Constant Time Sphere Indexing - 2019 : Part 1 and Part 2

Picking points on the hemisphere with a cosine density - 2019

Camera Rays - 2019

2D Signed Distance Field Basics - 2018

Spherical Gaussian Encoding - 2018

Monte Carlo Integration - 2018

Basic Math for Shaders - 2018

Math Library Experiences - 2019

The Map of Mathematics - 2017

How To Write A Maths Library In 2016 - 2016

Three Methods to Extract Frustum Points - 2016

Game Math Case Studies - 2015

Distant Spherical Area Light Sources - 2015

SIMD – Matrix3x3 Transpose - 2015

math-as-code - 2015

Slides: Mathematics for Gamedev - 2014

Interactive Introduction to Noise Functions - 2013

reed-util (math) - 2013

On Vector Math Libraries - 2013

Data-Oriented Design for Math - 2012

Essential Math for Games Programmers

Math for Game Programmers: Inverse Kinematics Revisited - 2015

Math for game programmers: Interaction with 3d geometry - 2013

Math for Game Programmers - 2013

Three Normal Mapping Techniques Explained For the Mathematically Uninclined - 2013

Linear algebra for game developers - One and Two - 2009

Interpolation Tricks - 2009

Mathematical Growing Pains - 2002

Vector maths – a primer for games programmers

Linear algebra for game developers ~ part 1

Jorge Rodriguez - Math and video games

Math for Game Programmers: Understanding Homogeneous Coordinates

Generating random points in a sphere

Normals and the Inverse Transpose, Part 3: Grassmann On Duals

Game Math: Deriving the Slerp Formula

http://allenchou.net/game-math-series/

Why Clip Transformed Vertices in Clip-Space?

hacking a generic ray-triangle intersector

How to ray-intersect a transformed geometry, without actually transforming it: a geometric illustration

A Fun 2d Rotation Matrix Derivation

Normal matrices are overrated

Matrices for Tech Artists, non Affine Transformations

Matrices for Tech Artists, a Cheat Sheet

Dot products and planes

Dot product and its relationship to matrices

Klein

Topics in Quantization for Games

http://cbloomrants.blogspot.com/2020/09/topics-in-quantization-for-games.html

Projective Geometric Algebra

http://projectivegeometricalgebra.org/