mathVis

mathVis is a Streamlit-powered educational app for exploring and visually understanding fundamental geometrical objects from linear and discrete optimization, such as convex hulls, polyhedra, and cones.
The app gives graphical representations, intuitive descriptions, and mathematical explanations for each object.

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Features

• Interactive selection of geometric objects: Convex Hull, Conical Hull, Convex Cone, Polytope, Polyhedral Cone, and more.
• Visualization of each object using Matplotlib.
• Clear descriptions and mathematical (LaTeX-formatted) explanations.
• Powered by Streamlit for instant web-based interactivity.
• Modular code: Easily add new objects as Python modules in the graphs/ folder.

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Demo

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Geometric Structures: Comparison Table

Structure	Convex?	Bounded?	Generators	Description
Convex Hull	Yes	Yes (if finite set)	Points	Smallest convex set containing a given set of points.
Conical Hull	Yes	No	Vectors (finite set)	All non-negative combinations of given vectors.
Convex Cone	Yes	No (except $\{0\}$)	Directions/rays (possibly infinite)	Any set closed under non-negative scaling/addition.
Polyhedral Cone	Yes	No (except $\{0\}$)	Vectors (finite set)	Convex cone defined by finitely many linear inequalities.
Polyhedron	Yes	Not always	Faces/vertices/edges	Solution set to finitely many linear inequalities.
Polytope	Yes	Yes	Vertices (finite set)	Bounded polyhedron; convex hull of a finite set of points.

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Getting Started

Prerequisites

• Python 3.8+
• pip

Installation

Clone this repository:

git clone https://github.com/IhebDridi/mathVis.git
cd mathVis

Install dependencies:

pip install -r requirements.txt

Run Locally

streamlit run MainStreamLit.py

Your web browser will open automatically. Use the sidebar to select a geometric object and view its visualization, description, and mathematical explanation.

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Folder Structure

mathVis/
│
├── MainStreamLit.py          # Main Streamlit app
├── graphs/                   # Individual Python modules for each graph type
│    ├── ConvexHull2D.py
│    ├── Polytope.py
│    └── ...
├── requirements.txt
├── README.md

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Add New Graph Types

1. Create a new Python file in graphs/, e.g., MyPolyhedron.py.
2. Define a function plot_mypolyhedron that returns (fig, description, math_explanation).
3. The app will automatically load new graph types at startup!

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Deploy on Streamlit Community Cloud

• Push your repo to GitHub.
• Go to https://streamlit.io/cloud.
• Link your repo and deploy.
• Updates auto-deploy when you push new changes.

See the official docs for more details.

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Credits

• Built with Streamlit
• Mathematical algorithms from scipy and numpy
• Visualization by matplotlib

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License

MIT License

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Contributing

Open an issue or pull request to suggest new geometries, fix bugs, or add documentation!

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Live Demo

🚀 Try the app online:
https://mathvis-8fot3lo7zuzehveqhsrdld.streamlit.app/

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Enjoy visualizing mathematics!