Luding Suspension Bridge Pedestrian Movement Analysis

Parametric curve modeling of pedestrian movement on the Luding Suspension Bridge using PCA and polynomial fitting in 3D space. Includes data visualization, dimensionality reduction, projection, and reconstruction in the original coordinate system.
This project analyzes the movement of pedestrians across the Luding Suspension Bridge in China using a dataset of 3D coordinates. The bridge follows a catenary curve and is modeled using dimensionality reduction and curve fitting techniques in $R^3$
The main objectives of the project include:

• Importing and visualizing the raw 3D data points.
• Applying Principal Component Analysis (PCA) to identify the plane in which the curve lies.
• Projecting the data onto this plane for simplification.
• Finding an orthogonal transformation to align the plane with a coordinate plane.
• Fitting a polynomial curve to the projected data using Gaussian approximation.
• Reconstructing the curve in the original coordinate system using inverse transformations.

The final output is a parametric equation representing the curve in $R^3$, along with the matrix of coefficients in the chosen polynomial basis. This repository contains all the code, visualizations, and mathematical steps involved in achieving these goals.