Surface-Estimation-via-Monte-Carlo-Algorithm

Overview

This Python project is a Pygame-based tool for interactively tracing shapes on a map and estimating their real-world area using a Monte Carlo sampling method. It was originally created as a demonstration tool to challenge flat-Earth proponents, by allowing users to draw regions on a "flat Earth" map and compute their real surface area — revealing inconsistencies that arise from projecting a spherical Earth onto a 2D plane.

---

Features

• Draw custom contours (polygons) with the mouse
• Set a real-world scale by clicking on a map's known distance (e.g., a scale bar)
• Estimate the enclosed area (in km²) using Monte Carlo integration
• Real-time updates during computation
• Handles open contours by automatically treating them as closed for the area calculation

---

Requirements

• Python 3.x
• Pygame (install via pip install pygame)

---

Setup & Launch

1. Clone or download this repository.

2. Ensure you have Pygame installed:

   pip install pygame

3. Modify the image path in the code to point to your local map image file:

   image_path = "/your/path/to/flat_earth.png"

4. Run the script:

   python your_script.py

---

How to Use

Step 1 — Drawing the Region

• Left-click and drag to draw a contour (polygon) on the map.
• The red line represents your current region.
• Release the mouse button to complete the trace.
• You can draw multiple traces if needed.

Note: Even if your trace appears open, the Monte Carlo method treats the region as closed by logically connecting the first and last points.

---

Step 2 — Setting the Scale

To convert from pixels to kilometers, you must define the scale:

1. Press Enter to enter scale measurement mode.
2. Left-click once at the start of the scale bar on the map.
3. Left-click again at the end of the scale bar.
4. A green line will appear, and you will be prompted to type the real-world distance in kilometers (e.g., 100).
5. Press Enter again to validate.

This sets the pixel-to-kilometer ratio used for accurate area estimation.

---

Step 3 — Estimating Area

• Once you've drawn your contour and set the scale, press Enter again to launch the Monte Carlo simulation.
• The tool randomly generates 100,000 sample points within the bounding box of your region and tests whether they lie inside the drawn shape.
• The estimated area in km² will be shown at the top-left of the screen and printed in the terminal.

---

Behind the Scenes: How It Works

Image and Display

• The tool loads a custom map image (.png) and uses its dimensions to size the Pygame window.
• Drawing is layered on top of the map surface.

Drawing and Storing Contours

• Traces are recorded as lists of point tuples (x, y).
• All user-drawn traces are stored in the traces list.
• Each time the mouse is moved while pressed, new points are added to the current trace.

Measuring Scale

• When measuring is enabled, two mouse clicks are interpreted as endpoints of a known-length segment.
• The pixel distance between these two points is computed and stored.
• The user is prompted to input the real distance in kilometers.
• A ratio (scale_ratio) is calculated in km/pixel and used for area conversion.

Monte Carlo Estimation

• The bounding box of all points is computed.
• 100,000 random points (num_samples = 100000) are generated inside this bounding box.
• Each point is tested using the ray casting algorithm to determine if it lies inside the polygon.
• The ratio of points inside the region vs. total samples gives the approximate pixel area.
• This area is converted to km² using the square of the scale ratio.

Automatic Contour Closure

• Even if the drawn contour is visually open, it is treated as closed by connecting the last point back to the first during inside/outside testing.
• This ensures the region is always interpreted as a proper polygon for area calculation.

---

Controls Summary

Key / Action	Function
Left Click & Drag	Draw a contour
Enter	Toggle between drawing, measuring, and launching estimation
Delete	Remove last trace
Backspace	Edit typed scale value
Escape	Quit the program

---

Example Use Case

Using a "flat Earth" map (azimuthal equidistant projection), you can:

• Trace the actual shape of a continent or region.
• Define a known scale from the map's scale bar.
• Compute the estimated area.
• Compare it to the real-world value to illustrate distortion due to projection — an inconsistency in the flat Earth model.

---

Limitations

• The estimation is probabilistic and might vary slightly due to randomness.
• The accuracy depends on the number of samples (set to 100,000 by default).
• It currently supports only 2D polygon tracing; no elevation or 3D projection handling.

---

Author & Purpose

This tool was developed to visually and mathematically challenge the flat Earth model by Hugo Alexandre (@Hugo_GW), demonstrating how projected maps distort real distances and areas. By using actual map scales and comparing computed areas, it serves as a simple but powerful educational and debunking tool.

---

Illustrations

Here are some illustration to understand how the code works and the several steps to estimate surfaces and aeras