/*! \mainpage G22-2025-Final Project Main Page

\section overview Overview
This is the Doxygen Python documentation for Team G22's Multi-Projector System for Semester 2025. 
This documentation provides comprehensive information about the system's architecture, classes, 
and implementation details.

\section documentation_structure Documentation Structure
- \b Classes \b Section: Contains detailed descriptions of all classes, structs, unions, interfaces, 
  functions, and variables used in the system.
- \b Files \b Section: Lists all documented source files with brief descriptions and inter-file dependencies.
- \b Technical \b Details: Explains the mathematical foundations, algorithms, and techniques implemented 
  in our project.

\section alpha_blending Alpha Blending 
When multiple projectors overlap, the overlapping regions receive illumination from multiple sources, 
resulting in excessively bright areas. Alpha blending mathematically reduces this illumination to achieve 
uniform brightness across the entire projection surface.

The image below illustrates the problem that occurs without alpha blending:

\image html alphablending.PNG "Visualization of Overlap Without Alpha Blending." width=600px

\section linear_blending Linear Blending
Linear alpha blending, as the name suggests, reduces the alpha of the image linearly with distance from the start of the overlap region:
- Left projector alpha curve: \f$ \mathit{Left} = 1 - \frac{x}{2} \f$
- Right projector alpha curve: \f$ \mathit{Right} = \frac{1}{2}(x + 1) \f$

\image html linearblending.PNG "Linear Blending." width=400px

\section quadratic_blending Quadratic Blending
Quadratic blending creates a smoother, parabolic transition:
- Left projector alpha curve: \f$ \mathit{Left} = (1 - x)^2 \f$
- Right projector alpha curve: \f$ \mathit{Right} = x^2 \f$

\section gaussian_blending Gaussian Blending
Gaussian blending uses the error function for the most natural, bell-curve transition:
- Left projector alpha curve: \f$ \mathit{Left} = 1 - \mathit{Right} \f$
- Right projector alpha curve: \f$ \mathit{Right} = \frac{4(1 + \mathit{erf}(x - \frac{1}{2}))}{\sqrt{2}} \f$

*/



