Stiefel Manifolds and Polygons

Overview

This is an implementation of the ideas exposed in the article Stiefel Manifolds and Polygons (SMP) published by Clayton Shonkwiller in 2019. The goal is to describe an identification of polygons with points in $\text{St}_2(\mathbb R^k)$. With that identification in hand, in this project we will:

• Use the tools in SMP to define what a random polygon is
• Generate random polygons
• Make random polygons convex

Installation

To install the package, navigate to the project root and run:

pip install -e .

pip install -r requirements.txt

Requirements

• numpy == 1.16.4
• matplotlib==1.3.1
• scipy==3.1.1

How to Run

1. Clone this repository
2. Install the necessary dependencies
3. Run the examples provided in the examples/ directory to test the functionality

Next Steps

Potential future developments for this project include:

• Implementing the algorithm for finding paths in the polygon space
• Implementing the algorithm for the generation of random planar tilings

Contributing

Feel free to contribute by opening a pull request. If you find any issues, please report them!