Triangle Matrix Transformation (SFML 3 + C++)

This project visualizes a 2D linear transformation of a triangle using SFML 3 in C++. The triangle is smoothly animated from its original coordinates to its transformed coordinates on a Cartesian plane.

This project was influenced by this high school question

Features

• Draws Cartesian axes on screen

• Displays an original triangle

• Applies a matrix transformation:

  x' = y
  y' = x − 2y
  

• Smooth step-by-step animation between original and transformed triangle

• Built using SFML 3 and MinGW (MSYS2 g++)

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Requirements

You must have the following installed:

1. C++ Compiler (MSYS2 MinGW)

Verify installation:

g++ --version

Expected example:

g++ (Rev8, Built by MSYS2 project) 15.x.x

If not installed:

• Install MSYS2
• Install toolchain:

pacman -S mingw-w64-ucrt-x86_64-gcc

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2. SFML 3 (GCC / MinGW build)

Download:

SFML-3.0.2-windows-gcc-...-64-bit.zip

Extract somewhere like:

F:/downloads/SFML-3.0.2/

Important folders:

include/   → header files
lib/       → libraries for linking
bin/       → required DLLs at runtime

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3. VS Code (optional but recommended)

Install extensions:

• C/C++ (Microsoft)

Configure compilerPath:

C:/msys64/ucrt64/bin/g++.exe

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How to Compile

Open PowerShell in the project folder and run:

C:/msys64/ucrt64/bin/g++.exe matrix.cpp `
  -IF:/downloads/SFML-3.0.2-windows-gcc-14.2.0-mingw-64-bit/SFML-3.0.2/include `
  -LF:/downloads/SFML-3.0.2-windows-gcc-14.2.0-mingw-64-bit/SFML-3.0.2/lib `
  -lsfml-graphics -lsfml-window -lsfml-system `
  -o matrix.exe

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How to Run

After compiling:

.\matrix.exe

If you see missing DLL errors, copy all files from:

SFML/bin/

into the same folder as:

matrix.exe

Then run again.

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📐 Mathematical Idea

A linear transformation matrix changes point coordinates:

[ x' ]   [ 0  1 ] [ x ]
[ y' ] = [ 1 -2 ] [ y ]

This project:

• Shows the original triangle
• Animates the continuous transformation
• Helps visualize matrix effects in geometry

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Project Structure

matrix_math/
│
├── matrix.cpp
├── matrix.exe (after compilation)
└── README.md

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Possible Improvements

• Show both original and transformed triangles
• Add grid lines
• Allow keyboard-controlled transformations
• Display matrix values on screen
• Support multiple transformation types:
  • Rotation
  • Scaling
  • Reflection
  • Shear

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Author

David Kingori