game-math

Mathematical library for game developers.
The library contains necessary elements of Matrix Algebra to enable working in 2D and 3D space.

Current feature support

• Math:
  • 2,3,4-dimensional Matrix/Vector algebra (math.h)
• Game specific:
  • 2D/3D Transformation utils to generate View/Transformation matrices in a 2D view space (utils.h)
• Numerical Methods (extension numerics)
  • Solver for initial value problems of (stiff) ordinary differential equations (ode.h)
    • Unified class for solvers (ODESolver)
    • Explicit Euler Method (ExplicitEuler.h)
    • Explicit 5 step Runge-Kutta-Method (ode45.h)
    • Trapezoid rule for odes (odeTrapez.h)
    • Backward differential formula (odeBDF2.h)
  • Solver for systems of linear equations (gaussSeidel.h)
  • Gauss-Jordan method to calculate inverse matrices (gaussJordan.h)
  • QR-Decomposition of matrices (qr.h)
  • Singular Value Decomposition (SVD) (svd.h)
  • Fractals using numerical approximations (Fractals.h)
    • NewtonFractal
    • Mandelbrot
  • Newton method to approximate the zero-value for a given function based on an initial value newton.h
  • Function Interpolation/Approximation
    • 1D Interpolation
      • Polynomial Interpolation (PolynomialBase)
        • MonomBase
        • LagrangeBase
        • NewtonBase
      • Spline Interpolation
        • Spline: implements Natural cubic spline, as well as a B-Spline capable of interpolating 3D values
    • 2D/3D Interpolation
      • see Spline
  • Differential calculus (Differentiation.h)
  • Numerical Integration (Integration.h)
• (classic) Statistics:
  • Probability.h
  • Insurance.h
• Plot support (uses/requires gnuplot see include/math/visualization/README.md or Plot.h)
• Data Science:
  • Classification:
    • NCC: Nearest Centroid Classifier (linear classifier) (NCC.h)
    • KNN: K Nearest Neighbor Classifier (non-linear classifier) (KNN.h)
  • Neural networks
    • Feed Forward NNs
      • Perceptron classifier (Perceptron)
      • Adaline Neuron Classifier
        • using gradient decent method (AdalineGD)
        • using statistics gradient decent method (AdalineSGD)

Benchmarks

see /benchmarks/README.md

Matrix<int>:
finished computation with 9 elements and 5000000 * operations. elapsed time: 0.160372s
finished computation with 9 elements and 5000000 # operations. elapsed time: 0.0172873s
finished computation with 9 elements and 5000000 + operations. elapsed time: 0.145237s
mat3<int>:
finished computation with 9 elements and 5000000 * operations. elapsed time: 4.3e-08s
finished computation with 9 elements and 5000000 + operations. elapsed time: 5e-08s
Matrix<double>:
finished computation with 9 elements and 5000000 * operations. elapsed time: 0.132516s
finished computation with 9 elements and 5000000 # operations. elapsed time: 0.00899579s
finished computation with 9 elements and 5000000 + operations. elapsed time: 0.152282s
mat3<double>:
finished computation with 9 elements and 5000000 * operations. elapsed time: 5.2e-08s
finished computation with 9 elements and 5000000 + operations. elapsed time: 5e-08s
Matrix<float>:
finished computation with 9 elements and 5000000 * operations. elapsed time: 0.186274s
finished computation with 9 elements and 5000000 # operations. elapsed time: 0.00887903s
finished computation with 9 elements and 5000000 + operations. elapsed time: 0.146145s
mat3<float>:
finished computation with 9 elements and 5000000 * operations. elapsed time: 7.1e-08s
finished computation with 9 elements and 5000000 + operations. elapsed time: 8e-08s

Build requirements

gcc, cmake, clang

Installation

1. Download repository git clone git@github.com:/philsupertramp/game-math
2. Integration into your project

Only CMake fully tested

cmake:

in your CMakeLists.txt add

link_libraries(math-lib)
include_directories(math/include)

Usage

After linking the library correctly one is able to include the main header file math.h

 {c++}
#include <math/math.h>

Although one can explicitly include parts

 {c++}
#include <math/vec/vec2.h>

Extensions

Currently there are two different implementations of matrices/vectors

Implementation 1)

Game dev oriented. 2, 3 and 4 dimensional vector/matrix implementations.
Tightly packed data to allow minimal memory usage. see ./include/math/vec and ./include/math/mat for implementation details.

Implementation 2)

Matrix<T> (see ./include/math/Matrix.h) represents a m x n-Matrix of data of type T

a specific data science and numerics implementation.
Capable of Matrix-Vector and Matrix-Multiplication, it also contains data science specific algorithms and statistical methods.

Extensions

The library is split into multiple content seperated module. Each module is nested in the root directory math/.
Each sub-directory contains a README file with instructions how to use the module and if it has dependencies.

Adding extensions to library

To activate modules use the MATH_EXTENSIONS compile argument.

Example build command adding numerics module and building test suite:

mkdir -p build
cmake -DMATH_EXTENSIONS=numerics --build math/build -- -j 3 .

Development

Feel free to contribute to the project!

How to contribute

• first time contributors
  • fork the project
  • create a PR based on your repository
• known contributors
  • create PR based on master branch

NOTE: please run make lint prior to submitting your code!
This requires clang-format>=11.0.0

License

The project is under MIT-License see LICENSE for more

Acknowledgements