PFEE: Gradient Vector Fields of Discrete Morse Functions are Minimum Spanning Forest

This project aims to build an end-to-end visualization program that implements the algorithms of the research paper Discrete Morse Functions and Watersheds and visually proves that the Minimum Spanning Forest (MST) of the dual graph of a simplicial stack (or a discrete Morse function) is equivalent to the Gradient Vector Field (GVF) of the initial function. The solution is built using Python 3, VTK (Visualization Toolkit) and Paraview for the rendering.

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Project architecture

This is a schema of the project's main architecture.

Format

The application generate CSV files containing coordinates from the given function.

Show CSV Format

Points

Node Number	X	Y	Z	Weight
int	float	float	float	int

Lines

P1	P2	Weight
Node Number	Node Number	int

Triangles

S1	S2	S3	Weight
Node Number	Node Number	Node Number	int

All the files generated by the algorithms are in vtu format and can be opened in paraview.

Installation

Download the python libraries listed in requirements.txt.

$ pip install -r requirements.txt

Python

To launch the application.

$ python main.py

The available options are:

• -s --size: specify the size of the grid, default is 9.
• -r --resolution: specify the size of a single triangle edge. To make it higher, enter a value < 1. Default is 1.
• -m --minimas: specify the method to compute minimas
  • 0 -> strictly inferior
  • 1 -> less than or equal to
  • 2 -> forced isolated minima with strict lower
  • 3 -> isolated forced minima with less than or equal to

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othman.elbaz@epita.fr  ·  william.guillet@epita.fr  ·  vincent.courty@epita.fr