Links

Here you will find links for the topic Game Development.

Here you will find links for the topic Mathematics.

Artificial Intelligence

Amit’s A Pages  
Behavioral Mathematics for Game AI  
Bias-Variance Decomposition  
Heuristics of Min Cost Paths  
Intro to Lambda Calculus  
Intro to Neural Networks  
Lambda Calculus  
Mathematics of Neural Networks  
Pathfinding in Computer Games  
Perceptron Algorithm  
Predicate Logic  
Situation Calculus  
Smooth perceptron algorithm  
Video Games and AI  

Basics

3D Math - Coordinate Systems  
Abstract and Linear Algebra  
Elementary Linear Algebra  
Intro Linear Algebra  
OpenGL Coordinate System Tutorial  

Calculus

Basic Calculus Refresher  
Calculus Review and Tutorial  
Elements of Calculus  
Intro to Differential Calculus  
Intro to Partial Differential Equations - Moore  
Intro to Partial Differential Equations - Uni-Arizona  
Intro to Partial Differential Equations - Urroz  
Intro to Partial Differential Equations  
PDE Primer  
Topics in Calculus  

Collision

Building the Convex Hull  
Collision Detection with Polygons  
Collision Detection  
Collision  
Everything you want to know about CD -ppt  
Fast and Robust GJK  
GJK (Gilbert–Johnson–Keerthi)  
Intersection Detection  
Object-Object Intersection  
Physics and Collision Detection  
Point-Line-Plane Distances  
Quick Collision Detection of Polytopes  
Ray Casting against Convex Objects  
Reducing the Impact in Real-time  
Simple Intersection Tests For Games  
Theory & Practice of CD  
Wolfram - Point-Line Distance -2D  
Wolfram - Point-Line Distance -3D  

Curves & Surfaces

Bezier Curves and Surfaces  
Bezier Patches  
Bezier Subdivision and De Casteljau’s Algo  
Catmull-Rom splines  
De Casteljau Algorithm  
Introduction to Catmull-Rom Splines  
Rendering Cubic Bezier Patches  
Wolfram - B-Spline

Fluids

Diffusion  
Environmental Hydrology  
Fick's Laws The Math of Diffusion  
Gerstner’s Water Wave  
GPU Gems - Fluid Dynamics Sim on the GPU  
GPU Gems 3 - RT Sim and Render of 3D Fluids  
Navier-Stokes Equations in Fluid Mechanics  
Navier-Stokes Equations  
Real-Time Volumetric Smoke  
Smoothed Particle Hydrodynamics  
The Navier-Stokes Equation  
The Shallow Water Equations - Dawson  
The Shallow Water Equations - Gerber  
The Shallow Water Equations - Moler  
The Shallow Water Equations - Randall  

Fourier Transformation

Cooley-Tukey  
Fast Fourier Transform - Batenkov  
Fast Fourier Transform - Bourke  
Fast Fourier Transform - CMLab  
Fast Fourier Transform - Smith  
Fast Fourier transform  
Fourier Transform  
Math of the Discrete Fourier Transform  
The Cooley-Tukey FFT Algo  
Wolfram - Fast Fourier Transform  
Wolfram - Fourier Transform  

Frustum

flipcode - Frustum Culling  
View frustum math  
View Frustum’s Shape  

Image Processing

Adaptive Edge Anti-Aliasing Filter
An Intro To Digital Image Processing  
Bayesian Edge-Detection  
Bayesian Image Processing  
Canny Edge Detection  
Edge Detection  
Efficient Gaussian blur with linear sampling  
Frei-Chen edge detector  
Gamma Correction A Story of Linearity  
Gamma Correction  
Image Processing a Pattern Recognition - vo3  
Image Processing a Pattern Recognition - vo4  
Image Processing a Pattern Recognition - vo5  
Sobel Edge Detection  
Sobel Edge Detector  
Sobel Edge  
Spatial Filters - Gaussian Smoothing  

Interpolation

Algorithms in Scientific Visualization  
GPWiki - Linear Interpolation  
Hermite Curve Interpolation  
Hermite Interpolation
Interpolation methods  

Lighting

Adaptive Logarithmic Mapping For HDR  
Cook-Torrance Reflectance Model  
D3DBook - Ashikhmin-Shirley  
D3DBook - Blinn-Phong  
D3DBook - Cook-Torrance  
D3DBook - Foundation and theory of lighting  
D3DBook - Oren-Nayar  
D3DBook - Strauss  
D3DBook - Ward  
Gamasutra - Volumetric Rendering in Realtime  
GPU Gems - Spatial BRDFs  
HDR in OpenGL  
Illumination Models  
Intro to BRDF-Based Lighting  
LogLuv Encoding for HDR  
Odwiki - ReflectanceFunctions  
Phong Lighting - OpenGL & Ray Tracing  
Physically-Based Reflectance for Games  
Ray Tracing - Graphics for the Masses  
Spherical Harmonic Lighting - Gritty Details  
Survey of Shading Models for RT Render  
Tangent Space Calculation  
Tone Reproduction for Digital Images
What Is the Rendering Equation  
XNA Shader Programming – Refraction  

Matrices

3D Math - Matrices  
3D Matrix Formulas  
Matrices - Translation & Rotation  
Matrix Algebra -doc  
Matrix Algebra Operations  
Matrix and Quaternion FAQ  
Review of Arrays, Vectors and Matrices  
Summary Matrix Algebra  
The Cg Tutorial - Transformations  
The Mathematics of the 3D Rotation Matrix  
World, View and Projection Matrix  

Numerical Analysis

FD, FE and FV - PDEs
Intro to FEM  
Intro to Numerical Analysis - Arnold  
Intro to Numerical Analysis  
Iterative Methods for Solving Linear Systems  
Jacobi and Gauss-Seidel Iteration  
Large eigenvalue problems  
Maclaurin Series  
Monte Carlo integration - Edwards  
Monte Carlo integration - Nordlund  
Monte Carlo Integration  
Multigrid Methods  
Multigrid Relaxation  
Numerical Analysis - FDM  
Numerical Methods for Differential Equations  
Numerical Methods in Fluid Dynamics  
Numerical Solutions of ODEs  
Runge-Kutta Methods  
Taylor Series - ODE Initial Value Problems  
Taylor Series Approximations  

Physics

Advanced mechanics  
Building a 2D Physics Engine for MASON  
Classical Mechanics - Shapiro  
Gamasutra - Exploring Spring Model  
Gravity  
Integration Basics  
Iterative Dynamics  
Lectures4you.de - Physik  
Mechanics of a Rigid Body  
Multibody Dynamics Animation  
Pixar Research - Physically Based Modeling  
Rigid Body Dynamics of Interacting Particles  
Rotational Motion of a Rigid Body
RT Physics Simulation Engines  
Time Integration

Planes

Hesse normal form  
Intersection of Lines and Planes  
Line-plane intersection tutorial  
Lines - Planes - Equations - Distances - Angles  
Plane Equation  
Point-Plane Collision Detection  
Wolfram - Plane  
Wolfram - Point-Plane Distance  

Polygone

Constrained Delaunay Triangulation  
Delaunay Triangulation  
Marching Cubes  
Survey of the marching cubes algorithm  
Voronoi and Delaunay Diagrams  
Voronoi and Delaunay Techniques  

Probability Theory

Discrete Probability Distributions  
Probability Theory - Logic of Science  
Probability Theory  
Pseudorandom Number Generators  
Random Numbers  
Review of Probability Theory  
Statistics Tutorial - Poisson Distribution  
Statistics Tutorial - Probability Distributions  
The Gaussian (Normal) Distribution  
Wolfram - Normal Distribution  
Wolfram - Poisson Distribution  

Quaternions

Application of Quaternions  
gamedev.net - Quaternion Powers  
Quaternions and 3D Rotations  
Using Quaternions to Represent Rotation  
Wolfram - Quaternion  

Terrain

Generating Random Fractal Terrain  
Landscape Generation and Smoothing  
LSystems Tutorial For Artists -doc  
Perlin Noise  
Realtime Procedural Terrain Generation  
Roads  
Simulation of Stone-, and Rockfalls  
Synth and Render of Eroded Fractal Terrains  
Triangle Strip preserving LOD  
Virtual Terrain Project  

Vector Analysis

Elements of Vector Analysis - Gibbs  
Elements of vector analysis - Wacker  
Google Books - Vector analysis  
Vector Analysis - Callen  
Vector Analysis - Uni Bochum  
Vector Analysis - Uni-Ben-Gurion  

Vectors

3d Vector Mathematics  
Linear algebra for game developers  
Vector Algebra  
Vector Math for 3D Computer Graphics - Kjell  
Vector Math for 3D Computer Graphics  
Wolfram - Normal Vector  

Wavelet & SH

A Gentle Intro to Wavelets  
An Intro to Wavelets and Haar Transform  
An Intro to Wavelets  
Coding the Haar Wavelet Transform  
Haar Wavelet Transform  
Importance Sampling Spherical Harmonics  
Introduction to Wavelet  
Spherical Harmonics  
Wavelets An Elementary Intro  
Wavelets for Computer Graphics  
Wavelets -ppt  
Wolfram - Spherical Harmonic  

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