🌍 Fourier Approximation of Geospatial Data

This project explores the application of Fourier Series to approximate complex geospatial shapes, specifically coastlines and land boundaries, using Python. By leveraging Fast Fourier Transform (FFT), the algorithm decomposes geospatial data into frequency components, reconstructing the original shape with a limited number of terms to balance accuracy and efficiency.

The method offers a compact representation of geographical features, which is particularly useful in data compression, geospatial analysis, and computational geometry - possibly even helping in spatial querying as it then relies on math.

---

📸 Media

---

🚀 Installation

Ensure you have Python installed. Then, install the required dependencies:

pip install numpy matplotlib scipy geopandas

---

📜 Usage

To run the script and visualize Fourier approximations of geospatial data:

python SGD_research.py

If the detailed geospatial data cannot be fetched, the script will generate a synthetic dataset automatically.

---

📊 Methodology

1. Data Acquisition: The script retrieves geospatial boundary data using GeoPandas.
2. Fourier Transform: The coordinates are converted into a complex plane representation, followed by applying Fast Fourier Transform (FFT).
3. Truncation and Reconstruction: By limiting the number of Fourier coefficients, the shape is reconstructed with varying levels of detail.
4. Visualization: Results are plotted using Matplotlib to compare original and approximated shapes.

This approach allows users to explore how different frequency components contribute to shape reconstruction and experiment with different levels of approximation.

---

🛠 Contributing

We welcome contributions! To get started:

1. Fork the repository 🍴
2. Clone your forked repo:

git clone https://github.com/your-username/Spatial_Storage_Fourier.git

3. Create a new branch for your feature:

git checkout -b feature-name

4. Make your changes & commit:

git commit -am "Added an awesome feature!"

5. Push to your branch:

git push origin feature-name

6. Open a Pull Request (PR) 🚀

---

⚡ Open for Expansion!

This project is open-source and ready for further improvements! Check out Work to be done - Do sort them as "Oldest First". Feel free to contribute and push this project further! 🚀🎨